%% This BibTeX bibliography file was created using BibDesk. %% https://bibdesk.sourceforge.io/ %% Created for Long Chen at 2025-11-27 16:00:19 -0800 %% Saved with string encoding Unicode (UTF-8) @unpublished{ChenGuoWeiZou2025PrecondNonlinearPDE, author = {Chen, Long and Guo, R. and Wei, J. and Zou, J.}, note = {Submitted}, title = {A Novel Preconditioning Framework for Solving Nonlinear PDEs based on Fenchel--Rockafellar Duality and Transformed Primal--Dual Techniques}, year = {2025}, bdsk-file-1 = 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@unpublished{ChenXu2025HNAGpp, author = {Chen, Long and Xu, Z.}, note = {Submitted}, title = {HNAG++: A Super-Fast Accelerated Gradient Method for Strongly Convex Optimization}, year = {2025}} @unpublished{ChenHuangZhangZhao2025StokesSuperconv, author = {Chen, Long and Huang, X. and Zhang, C. and Zhao, X.}, note = {Submitted}, title = {Superconvergent and Divergence-Free Finite Element Methods for Stokes Equation}, year = {2025}} @unpublished{ChenChenGaoHuangWei2025SmoothSpaces, author = {Chen, C. and Chen, Long and Gao, T. and Huang, X. and Wei, H.}, note = {Submitted}, title = {Implementation and Basis Construction for Smooth Finite Element Spaces}, year = {2025}, bdsk-file-1 = 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@unpublished{ChenXuWeiLuoYao2025AMDSplitting, author = {Chen, Long and Xu, Z. and Wei, J. and Luo, H. and Yao, Y.}, note = {Submitted}, title = {Accelerated Mirror Descent Method through Variable and Operator Splitting}, year = {2025}} @unpublished{XuChen2025AdaptiveAGD, author = {Xu, Z. and Chen, Long}, note = {Submitted}, title = {Adaptive Accelerated Gradient Descent Methods for Convex Optimization}, year = {2025}} @unpublished{ChenLuoWei2025AGMSplitting, author = {Chen, Long and Luo, H. and Wei, J.}, note = {Submitted}, title = {Accelerated Gradient Methods Through Variable and Operator Splitting}, year = {2025}} @unpublished{ChenHuang2024TangentNormalForms, author = {Chen, Long and Huang, X.}, note = {Submitted}, title = {Tangential Normal Decompositions of Finite Element Differential Forms}, year = {2024}} @article{ChenHuang2025HybridizableStress, author = {Chen, Long and Huang, X.}, journal = {Mathematics of Computation}, note = {To appear}, title = {Hybridizable Symmetric Stress Elements on the Barycentric Refinement in Arbitrary Dimensions}, year = {2025}} @article{ChenHuangParkWang2025PrimalSDGPolytopal, author = {Chen, Long and Huang, X. and Park, E. J. and Wang, R.}, doi = {10.1007/s10915-025-02998-8}, journal = {Journal of Scientific Computing}, number = {89}, title = {A Primal Staggered Discontinuous Galerkin Method on Polytopal Meshes}, volume = {104}, year = {2025}, bdsk-url-1 = {https://doi.org/10.1007/s10915-025-02998-8}} @article{ChenGuoWei2025TPDVarPrecond, author = {Chen, Long and Guo, R. and Wei, J.}, doi = {10.1137/24M1667245}, journal = {SIAM Journal on Scientific Computing}, title = {Transformed Primal--Dual Methods with Variable-Preconditioners}, year = {2025}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1137/24M1667245}} @article{CaoChenLee2025EdgeAveragedVEM, author = {Cao, S. and Chen, Long and Lee, S.}, doi = {10.1007/s10915-025-02984-0}, journal = {Journal of Scientific Computing}, number = {70}, title = {Edge-averaged Virtual Element Methods for Convection--Diffusion and Convection-Dominated Problems}, volume = {104}, year = {2025}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1007/s10915-025-02984-0}} @article{ChenHuangZhang2025DistCurlDivQuadCurl, author = {Chen, Long and Huang, X. and Zhang, C.}, doi = {10.1137/23M1617400}, journal = {SIAM Journal on Numerical Analysis}, number = {3}, title = {Distributional Finite Element curl div Complexes and Application to Quad Curl Problems}, volume = {63}, year = {2025}, bdsk-file-1 = 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@article{ChenHuang2025ComplexesFromComplexes, author = {Chen, Long and Huang, X.}, doi = {10.1090/mcom/4079}, journal = {Mathematics of Computation}, title = {Complexes from Complexes: Finite Element Complexes in Three Dimensions}, year = {2025}, bdsk-url-1 = {https://doi.org/10.1090/mcom/4079}} @article{ChenHuang2024HdivTensorsConstraints, author = {Chen, Long and Huang, X.}, doi = {10.1016/j.rinam.2024.100494}, journal = {Results in Applied Mathematics}, pages = {100494}, title = {H(div)-conforming Finite Element Tensors with Constraints}, volume = {23}, year = {2024}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1016/j.rinam.2024.100494}} @article{ChenChenHuangWei2024GeoDecompFaceEdge, author = {Chen, C. Y. and Chen, Long and Huang, X. H. and Wei, H. Y.}, doi = {10.4208/cicp.OA-2023-0249}, journal = {Communications in Computational Physics}, number = {4}, pages = {1045--1072}, title = {Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements}, volume = {35}, year = {2024}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1090/mcom/3859}} @article{XieCaoChenZhong2023AdaptiveMWG, author = {Xie, Y. and Cao, S. and Chen, Long and Zhong, L.}, doi = {10.1002/num.23027}, journal = {Numerical Methods for Partial Differential Equations}, number = {5}, pages = {3847--3873}, title = {Convergence and Optimality of an Adaptive Modified Weak Galerkin Finite Element Method}, volume = {39}, year = {2023}, bdsk-url-1 = {https://doi.org/10.1002/num.23027}} @article{ChenWei2023TPDNonlinearSaddle, author = {Chen, Long and Wei, J.}, doi = {10.1515/jnma-2022-0056}, journal = {Journal of Numerical Mathematics}, number = {4}, pages = {281--311}, title = {Transformed Primal--Dual Methods for Nonlinear Saddle Point Systems}, volume = {31}, year = {2023}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1515/jnma-2022-0056}} @article{CaoChenGuo2023ImmersedVEMMaxwell3D, author = {Cao, S. and Chen, Long and Guo, R.}, doi = {10.1142/S0218202523500112}, journal = {Mathematical Models and Methods in Applied Sciences}, number = {3}, pages = {455--503}, title = {Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions}, volume = {33}, year = {2023}, bdsk-file-1 = 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bdsk-url-1 = {https://doi.org/10.1142/S0218202523500112}} @article{CaoChenGuoLin2022ImmersedVEMElliptic2D, author = {Cao, S. and Chen, Long and Guo, R. and Lin, F.}, doi = {10.1007/s10915-022-01949-x}, journal = {Journal of Scientific Computing}, number = {12}, title = {Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions}, volume = {93}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1007/s10915-022-01949-x}} @article{ChenHuang2022DivDivArbitraryDim, author = {Chen, Long and Huang, X.}, doi = {10.1137/21M1433708}, journal = {SIAM Journal on Numerical Analysis}, pages = {1932--1961}, title = {Finite Elements for div and divdiv Conforming Symmetric Tensors in Arbitrary Dimensions}, volume = {60}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1137/21M1433708}} @article{WangZhengChenLinXu2022BlockTriangularSG, author = {Wang, D. and Zheng, B. and Chen, Long and Lin, G. and Xu, J.}, doi = {10.1016/j.cam.2022.114298}, journal = {Journal of Computational and Applied Mathematics}, pages = {114298}, title = {Block Triangular Preconditioning for Stochastic Galerkin Method}, volume = {412}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1016/j.cam.2022.114298}} @article{ChenHuang2022ElasticityComplex3D, author = {Chen, Long and Huang, X.}, doi = {10.1090/mcom/3739}, journal = {Mathematics of Computation}, pages = {2095--2127}, title = {A Finite Elements Elasticity Complex in Three Dimensions}, volume = {91}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3739}} @article{CaoChenHuang2022QuadCurlError, author = {Cao, S. and Chen, Long and Huang, X.}, doi = {10.1007/s10915-021-01705-7}, journal = {Journal of Scientific Computing}, number = {29}, title = {Error Analysis of a Decoupled Finite Element Method for Quad-Curl Problems}, volume = {90}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1007/s10915-021-01705-7}} @article{CaoChenGuo2021VEMMaxwell2D, author = {Cao, S. and Chen, Long and Guo, R.}, doi = {10.1142/S0218202521500652}, journal = {Mathematical Models and Methods in Applied Sciences}, number = {14}, pages = {2907--2936}, title = {A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh}, volume = {31}, year = {2021}, bdsk-url-1 = {https://doi.org/10.1142/S0218202521500652}} @article{LuoChen2021FromODEtoAFOM, author = {Luo, H. and Chen, Long}, doi = {10.1007/s10107-021-01713-3}, journal = {Mathematical Programming}, pages = {735--781}, title = {From Differential Equation Solvers to Accelerated First-Order Methods for Convex Optimization}, volume = {195}, year = {2021}, bdsk-url-1 = {https://doi.org/10.1007/s10107-021-01713-3}} @article{ChenHuang2021DivDiv3D, author = {Chen, Long and Huang, X.}, doi = {10.1090/mcom/3700}, journal = {Mathematics of Computation}, pages = {1107--1142}, title = {Finite Elements for divdiv-Conforming Symmetric Tensors in Three Dimensions}, volume = {91}, year = {2021}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3700}} @article{ChenHuWise2020FSDConvex, author = {Chen, Long and Hu, X. and Wise, S.}, doi = {10.1090/mcom/3526}, journal = {Mathematics of Computation}, pages = {2249--2282}, title = {Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems}, volume = {89}, year = {2020}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3526}} @article{ChenHuang2020NonconfVEM2mRn, author = {Chen, Long and Huang, X.}, doi = {10.1090/mcom/3498}, journal = {Mathematics of Computation}, pages = {1711--1744}, title = {Nonconforming Virtual Element Method for $2m$-th Order Partial Differential Equations in $\mathbb{R}^n$}, volume = {89}, year = {2020}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3498}} @article{CaoChen2019AnisotropicNonconfVEM, author = {Cao, S. and Chen, Long}, doi = {10.1137/18M1196455}, journal = {SIAM Journal on Numerical Analysis}, number = {3}, pages = {1058--1081}, title = {Anisotropic Error Estimates of the Linear Nonconforming Virtual Element Methods}, volume = {57}, year = {2019}, bdsk-url-1 = {https://doi.org/10.1137/18M1196455}} @article{WangWangChenHe2019DivergenceFreeWeakVEMStokesDarcy, author = {Wang, G. and Wang, F. and Chen, Long and He, Y.}, doi = {10.1016/j.cma.2018.10.022}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {998--1020}, title = {A Divergence Free Weak Virtual Element Method for the Stokes--Darcy Problem on General Meshes}, volume = {344}, year = {2019}, bdsk-url-1 = {https://doi.org/10.1016/j.cma.2018.10.022}} @article{ChenWang2019DivergenceFreeWeakVEMStokes, author = {Chen, Long and Wang, F.}, doi = {10.1007/s10915-018-0796-5}, journal = {Journal of Scientific Computing}, pages = {864--886}, title = {A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polyhedral Meshes}, volume = {78}, year = {2019}, bdsk-url-1 = {https://doi.org/10.1007/s10915-018-0796-5}} @article{ChenHuang2018HelmholtzDecoupling, author = {Chen, Long and Huang, X.}, doi = {10.1137/17M1145872}, journal = {SIAM Journal on Numerical Analysis}, number = {5}, pages = {2796--2825}, title = {Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions}, volume = {56}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1137/17M1145872}} @article{CaoChen2018AnisotropicVEMPolygonal, author = {Cao, S. and Chen, Long}, doi = {10.1137/17M1154369}, journal = {SIAM Journal on Numerical Analysis}, number = {5}, pages = {2913--2939}, title = {Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes}, volume = {56}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1137/17M1154369}} @article{ChenHuHuang2018HHJMultigrid, author = {Chen, Long and Hu, J. and Huang, X.}, doi = {10.1007/s10915-017-0636-z}, journal = {Journal of Scientific Computing}, pages = {673--696}, title = {Multigrid Methods for Hellan--Herrmann--Johnson Mixed Method of Kirchhoff Plate Bending Problems}, volume = {76}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1007/s10915-017-0636-z}} @article{ChenHuang2018VEMErrorCalcolo, author = {Chen, Long and Huang, J.}, doi = {10.1007/s10092-018-0249-4}, journal = {Calcolo}, number = {5}, title = {Some Error Analysis on Virtual Element Methods}, volume = {55}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1007/s10092-018-0249-4}} @article{ChenHuHuangMan2018ResidualElasticity, author = {Chen, Long and Hu, J. and Huang, X. and Man, H.}, doi = {10.1007/s11425-017-9181-2}, journal = {Science China Mathematics}, pages = {973--992}, title = {Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems}, volume = {61}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1007/s11425-017-9181-2}} @article{ChenWuZhongZhou2018MGVectorLaplacian, author = {Chen, Long and Wu, Y. and Zhong, L. and Zhou, J.}, doi = {10.1007/s10915-018-0697-7}, journal = {Journal of Scientific Computing}, number = {1}, pages = {101--128}, title = {Multigrid Preconditioners for Mixed Finite Element Methods of the Vector Laplacian}, volume = {77}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1007/s10915-018-0697-7}} @article{ChenWu2017AdaptiveHodge, author = {Chen, Long and Wu, Y.}, doi = {10.1137/16M1097912}, journal = {SIAM Journal on Numerical Analysis}, number = {6}, pages = {2905--2929}, title = {Convergence of Adaptive Mixed Finite Element Methods for Hodge Laplacian Equation without Harmonic Forms}, volume = {55}, year = {2017}, bdsk-url-1 = {https://doi.org/10.1137/16M1097912}} @article{HuangChenRui2018DarcyForchheimerMG, author = {Huang, J. and Chen, Long and Rui, H.}, doi = {10.1007/s10915-017-0466-z}, journal = {Journal of Scientific Computing}, number = {1}, pages = {396--411}, title = {Multigrid Methods for a Mixed Finite Element Method of the Darcy--Forchheimer Model}, volume = {74}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1007/s10915-017-0466-z}} @article{ChenHuHuang2018FASPLinearElasticity, author = {Chen, Long and Hu, J. and Huang, X.}, doi = {10.1090/mcom/3285}, journal = {Mathematics of Computation}, number = {312}, pages = {1601--1633}, title = {Fast Auxiliary Space Preconditioner for Linear Elasticity in Mixed Form}, volume = {87}, year = {2018}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3285}} @article{ChenWeiWen2017InterfaceFittedVEM, author = {Chen, Long and Wei, H. and Wen, M.}, doi = {10.1016/j.jcp.2017.01.004}, journal = {Journal of Computational Physics}, pages = {327--348}, title = {An Interface-Fitted Mesh Generator and Virtual Element Methods for Elliptic Interface Problems}, volume = {334}, year = {2017}, bdsk-url-1 = {https://doi.org/10.1016/j.jcp.2017.01.004}} @article{ChenHuHuang2016StabilizedMixedElasticity, author = {Chen, Long and Hu, J. and Huang, X.}, doi = {10.1515/cmam-2016-0035}, journal = {Computational Methods in Applied Mathematics}, title = {Stabilized Mixed Finite Element Methods for Linear Elasticity on Simplicial Grids in $\mathbb{R}^n$}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1515/cmam-2016-0035}} @article{ZhengChenHuChenNochettoXu2016FourthOrderParabolic, author = {Zheng, B. and Chen, L. P. and Hu, X. and Chen, Long and Nochetto, R. H. and Xu, J.}, doi = {10.1007/s10915-016-0189-6}, journal = {Journal of Scientific Computing}, number = {1}, pages = {201--226}, title = {Fast Multilevel Solvers for a Class of Discrete Fourth Order Parabolic Problems}, volume = {69}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1007/s10915-016-0189-6}} @article{WangChenZhou2016PostprocessingCH, author = {Wang, W. and Chen, Long and Zhou, J.}, doi = {10.1007/s10915-015-0101-9}, journal = {Journal of Scientific Computing}, number = {2}, pages = {724--746}, title = {Postprocessing Mixed Finite Element Methods for Solving Cahn--Hilliard Equation: Methods and Error Analysis}, volume = {67}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1007/s10915-015-0101-9}} @article{ChenNochettoOtarolaSalgado2016MultilevelFractional, author = {Chen, Long and Nochetto, R. H. and Otarola, E. and Salgado, A. J.}, doi = {10.1090/mcom/3089}, journal = {Mathematics of Computation}, number = {302}, pages = {2583--2607}, title = {Multilevel Methods for Nonuniformly Elliptic Operators and Fractional Diffusion}, volume = {85}, year = {2016}, bdsk-url-1 = {https://doi.org/10.1090/mcom/3089}} @article{Chen2015MGsaddleConstrained, author = {Chen, Long}, doi = {10.1016/j.camwa.2015.09.020}, journal = {Computers and Mathematics with Applications}, number = {12}, pages = {2854--2866}, title = {Multi-Grid Methods for Saddle Point Systems Using Constrained Smoothers}, volume = {70}, year = {2015}, bdsk-url-1 = {https://doi.org/10.1016/j.camwa.2015.09.020}} @article{ZuChenXin2015ResidualKPP, author = {Zu, P. and Chen, Long and Xin, J.}, doi = {10.1016/j.physd.2015.07.001}, journal = {Physica D: Nonlinear Phenomena}, pages = {37--44}, title = {A Computational Study of Residual KPP Front Speeds in Time-Periodic Cellular Flows in the Small Diffusion Limit}, volume = {311}, year = {2015}, bdsk-url-1 = {https://doi.org/10.1016/j.physd.2015.07.001}} @article{ChenWangWangYe2015ASMGWeakGalerkin, author = {Chen, Long and Wang, J. and Wang, Y. and Ye, X.}, doi = {10.1016/j.camwa.2015.04.016}, journal = {Computers and Mathematics with Applications}, number = {4}, pages = {330--344}, title = {An Auxiliary Space Multigrid Preconditioner for the Weak Galerkin Method}, volume = {70}, year = {2015}, bdsk-url-1 = {https://doi.org/10.1016/j.camwa.2015.04.016}} @article{ChenNochettoOtarolaSalgado2015FractionalAPosteriori, author = {Chen, Long and Nochetto, R. H. and Otarola, E. and Salgado, A. J.}, doi = {10.1016/j.jcp.2015.01.001}, journal = {Journal of Computational Physics}, pages = {339--358}, title = {A PDE Approach to Fractional Diffusion: A Posteriori Error Analysis}, volume = {293}, year = {2015}, bdsk-url-1 = {https://doi.org/10.1016/j.jcp.2015.01.001}} @article{ChenHuWangXu2015MGDistributiveOseen, author = {Chen, Long and Hu, X. and Wang, M. and Xu, J.}, doi = {10.4208/nmtma.2015.w09si}, journal = {Numerical Mathematics: Theory, Methods and Applications}, number = {2}, pages = {237--252}, title = {A Multigrid Solver Based on Distributive Smoother and Defect Correction for Oseen Problems}, volume = {8}, year = {2015}, bdsk-url-1 = {https://doi.org/10.4208/nmtma.2015.w09si}} @article{Chen2014FortinTH, author = {Chen, Long}, doi = {10.1016/j.camwa.2014.09.003}, journal = {Computers and Mathematics with Applications}, number = {10}, pages = {1368--1373}, title = {A Simple Construction of a Fortin Operator for the Two Dimensional Taylor--Hood Element}, volume = {68}, year = {2014}, bdsk-url-1 = {https://doi.org/10.1016/j.camwa.2014.09.003}} @article{ZhouChenHuangWang2015TwoGridCH, author = {Zhou, J. and Chen, Long and Huang, Y. and Wang, W.}, doi = {10.4208/cicp.231213.100714a}, journal = {Communications in Computational Physics}, number = {1}, pages = {127--145}, title = {An Efficient Two-Grid Scheme for the Cahn--Hilliard Equation}, volume = {17}, year = {2015}, bdsk-url-1 = {https://doi.org/10.4208/cicp.231213.100714a}} @article{ChenWangZhong2015TriangularMAC, author = {Chen, Long and Wang, M. and Zhong, L.}, doi = {10.1007/s10915-014-9916-z}, journal = {Journal of Scientific Computing}, number = {3}, pages = {716--744}, title = {Convergence Analysis of the Triangular MAC Scheme for Stokes Equations}, volume = {63}, year = {2015}, bdsk-url-1 = {https://doi.org/10.1007/s10915-014-9916-z}} @article{HateleyWeiChen2014CVT, author = {Hateley, J. and Wei, H. and Chen, Long}, doi = {10.1007/s10915-014-9894-1}, journal = {Journal of Scientific Computing}, title = {Fast Methods for Computing Centroidal Voronoi Tessellations}, year = {2014}, bdsk-url-1 = {https://doi.org/10.1007/s10915-014-9894-1}} @article{ZhouHuZhongShuChen2014TwoGridMaxwell, author = {Zhou, J. and Hu, X. and Zhong, L. and Shu, S. and Chen, Long}, journal = {SIAM Journal on Numerical Analysis}, number = {4}, pages = {2027--2047}, title = {Two-Grid Methods for Maxwell Eigenvalue Problems}, volume = {52}, year = {2014}} @article{WeiChenHuangZheng2014AMRInterface, author = {Wei, H. and Chen, Long and Huang, Y. and Zheng, B.}, journal = {SIAM Journal on Scientific Computing}, number = {4}, pages = {A1478--A1499}, title = {Adaptive Mesh Refinement and Superconvergence for Two Dimensional Interface Problems}, volume = {36}, year = {2014}} @article{ChenWangYe2014APosterioriWG, author = {Chen, Long and Wang, J. and Ye, X.}, journal = {Journal of Scientific Computing}, number = {2}, pages = {496--511}, title = {A Posteriori Error Estimates for Weak Galerkin Finite Element Methods for Second Order Elliptic Problems}, volume = {59}, year = {2014}} @article{WuXieChen2013HybridStressFVM, author = {Wu, Y. and Xie, X. and Chen, Long}, journal = {International Journal of Numerical Analysis and Modeling}, number = {3}, pages = {634--656}, title = {Hybrid Stress Finite Volume Method for Linear Elasticity Problems}, volume = {10}, year = {2013}} @article{ChenWang2013FluxRecoveryFVM, author = {Chen, Long and Wang, M.}, journal = {Advances in Applied Mathematics and Mechanics}, number = {5}, pages = {705--727}, title = {Cell Conservative Flux Recovery and A Posteriori Error Estimate of Vertex-Centered Finite Volume Methods}, volume = {5}, year = {2013}} @article{WangChen2013MGStokesLSC, author = {Wang, M. and Chen, Long}, doi = {10.1007/s10915-013-9684-1}, journal = {Journal of Scientific Computing}, number = {2}, pages = {409--431}, title = {Multigrid Methods for the Stokes Equations Using Distributive Gauss--Seidel Relaxations Based on the Least Squares Commutator}, volume = {56}, year = {2013}, bdsk-url-1 = {https://doi.org/10.1007/s10915-013-9684-1}} @article{ChenHolstXuZhu2012LocalMLPrecond, author = {Chen, Long and Holst, M. J. and Xu, J. and Zhu, Y.}, journal = {Computing and Visualization in Science}, number = {5}, pages = {271--289}, title = {Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids}, volume = {15}, year = {2012}} @article{LoChenWangNie2012RDPatterns, author = {Lo, W. C. and Chen, Long and Wang, M. and Nie, Q.}, journal = {Journal of Computational Physics}, number = {15}, pages = {5062--5077}, title = {A Robust and Efficient Method for Steady State Patterns in Reaction--Diffusion Systems}, volume = {231}, year = {2012}} @article{WuChenXieXu2012VcycleAnisotropic, author = {Wu, Y. and Chen, Long and Xie, X. and Xu, J.}, journal = {IMA Journal of Numerical Analysis}, number = {4}, pages = {1329--1347}, title = {Convergence Analysis of V-Cycle Multigrid Methods for Anisotropic Elliptic Equations}, volume = {32}, year = {2012}} @article{ZhongChenShuWittumXu2012AdaptiveEdgeMaxwell, author = {Zhong, L. and Chen, Long and Shu, S. and Wittum, G. and Xu, J.}, journal = {Mathematics of Computation}, number = {278}, pages = {623--642}, title = {Quasi-Optimal Convergence of Adaptive Edge Finite Element Methods for Three Dimensional Indefinite Time-Harmonic Maxwell's Equations}, volume = {81}, year = {2012}} @article{ChenNochettoXu2011GradedBisection, author = {Chen, Long and Nochetto, R. H. and Xu, J.}, journal = {Numerische Mathematik}, number = {1}, pages = {1--34}, title = {Optimal Multilevel Methods for Graded Bisection Grids}, volume = {120}, year = {2011}} @article{ChenHolst2011ODTMeshOpt, author = {Chen, Long and Holst, M. J.}, journal = {Computer Methods in Applied Mechanics and Engineering}, pages = {967--984}, title = {Efficient Mesh Optimization Schemes Based on Optimal Delaunay Triangulations}, volume = {200}, year = {2011}} @article{WeiChenHuang2010LaplaceBeltrami, author = {Wei, H. and Chen, Long and Huang, Y.}, journal = {SIAM Journal on Numerical Analysis}, number = {5}, pages = {1920--1943}, title = {Superconvergence and Gradient Recovery of Linear Finite Elements for the Laplace--Beltrami Operator on General Surfaces}, volume = {48}, year = {2010}} @article{ChenZhang2010CoarseningNVB, author = {Chen, Long and Zhang, C.-S.}, journal = {Journal of Computational Mathematics}, number = {6}, pages = {767--789}, title = {A Coarsening Algorithm on Adaptive Grids by Newest Vertex Bisection and Its Applications}, volume = {28}, year = {2010}} @article{SunChenXu2010AdaptiveFEMConvection, author = {Sun, P. and Chen, Long and Xu, J.}, journal = {Journal of Scientific Computing}, number = {1}, pages = {24--43}, title = {Numerical Studies of Adaptive Finite Element Methods for Two Dimensional Convection-Dominated Problems}, volume = {43}, year = {2010}} @article{ZhongShuChenXu2010AdaptiveEdgeHcurl, author = {Zhong, L. and Shu, S. and Chen, Long and Xu, J.}, journal = {Numerical Linear Algebra with Applications}, number = {2--3}, pages = {415--432}, title = {Convergence of Adaptive Edge Finite Element Methods for $H(\mathrm{curl})$--Elliptic Problems}, volume = {17}, year = {2010}} @article{Chen2010HighOrderFVM, author = {Chen, Long}, journal = {SIAM Journal on Numerical Analysis}, number = {6}, pages = {4021--4043}, title = {A New Class of High Order Finite Volume Methods for Second Order Elliptic Equations}, volume = {47}, year = {2010}} @article{ChenLi2010SuperconvGraded, author = {Chen, Long and Li, H.}, journal = {Journal of Computational Mathematics}, pages = {11--31}, title = {Superconvergence of Gradient Recovery Schemes on Graded Meshes for Corner Singularities}, volume = {28}, year = {2010}} @article{ChenHolstXu2009AdaptiveMixedFEM, author = {Chen, Long and Holst, M. J. and Xu, J.}, journal = {Mathematics of Computation}, pages = {35--53}, title = {Convergence and Optimality of Adaptive Mixed Finite Element Methods}, volume = {78}, year = {2009}} @article{Chen2008OptimalSimplex, author = {Chen, Long}, journal = {East Journal of Approximation}, number = {3}, pages = {271--284}, title = {On Minimizing the Linear Interpolation Error of Convex Quadratic Functions and the Optimal Simplex}, volume = {14}, year = {2008}} @article{ChenWangWu2008StreamlineDiffusionTurning, author = {Chen, Long and Wang, Y. and Wu, J.}, journal = {Journal of Computational and Applied Mathematics}, pages = {712--724}, title = {Stability of a Streamline Diffusion Finite Element Method for Turning Point Problems}, volume = {220}, year = {2008}} @article{ChenXu2008AdaptedFEMSinguPerturbed, author = {Chen, Long and Xu, J.}, journal = {Numerische Mathematik}, number = {2}, pages = {167--191}, title = {Stability and Accuracy of Adapted Finite Element Methods for Singularly Perturbed Problems}, volume = {109}, year = {2008}} @article{ChenHolstXu2007PBNonlinear, author = {Chen, Long and Holst, M. J. and Xu, J.}, journal = {SIAM Journal on Numerical Analysis}, number = {6}, pages = {2298--2320}, title = {The Finite Element Approximation of the Nonlinear Poisson--Boltzmann Equation}, volume = {45}, year = {2007}} @article{ChenSunXu2007OptimalAnisotropicLp, author = {Chen, Long and Sun, P. and Xu, J.}, journal = {Mathematics of Computation}, number = {257}, pages = {179--204}, title = {Optimal Anisotropic Simplicial Meshes for Minimizing Interpolation Errors in $L^p$-Norm}, volume = {76}, year = {2007}} @article{JiangShuHuangChen2007ThreeTemps, author = {Jiang, J. and Shu, S. and Huang, Y. and Chen, Long}, journal = {Chinese Journal of Computational Physics}, number = {1}, pages = {19--28}, title = {A Mesh Adaptive Method for Two Dimensional Heat Conduction Equations with Three Temperatures}, volume = {24}, year = {2007}} @article{Chen2006SuperconvTetra, author = {Chen, Long}, journal = {International Journal of Numerical Analysis and Modeling}, number = {3}, pages = {273--282}, title = {Superconvergence of Tetrahedral Linear Finite Elements}, volume = {3}, year = {2006}} @article{Chen2005SphereCoveringPolytope, author = {Chen, Long}, journal = {Journal of Approximation Theory}, number = {1}, pages = {134--145}, title = {New Analysis of the Sphere Covering Problems and Optimal Polytope Approximation of Convex Bodies}, volume = {133}, year = {2005}} @article{ChenXu2004OptimalDelaunay, author = {Chen, Long and Xu, J.}, journal = {Journal of Computational Mathematics}, number = {2}, pages = {299--308}, title = {Optimal Delaunay Triangulations}, volume = {22}, year = {2004}} @inproceedings{WeiChen2025AORHB, author = {Wei, J. and Chen, Long}, booktitle = {Proceedings of the International Conference on Learning Representations (ICLR)}, title = {Accelerated Over-Relaxation Heavy-Ball Method: Achieving Global Accelerated Convergence with Broad Generalization}, year = {2025}} @inproceedings{GuoCaoChen2023TransformerBVP, author = {Guo, R. and Cao, S. and Chen, Long}, 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@inproceedings{KiaWeiChen2023ACC, author = {Kia, S. and Wei, J. and Chen, Long}, booktitle = {Proceedings of the 2023 American Control Conference (ACC)}, title = {Distributed Optimal Resource Allocation Using Transformed Primal--Dual Method}, year = {2023}, bdsk-file-1 = 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@inproceedings{NguyenSuliafuOsherChenWang2021FMMformer, author = {Nguyen, T. M. and Suliafu, V. and Osher, S. J. and Chen, Long and Wang, B.}, booktitle = {Advances in Neural Information Processing Systems (NeurIPS)}, title = {FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention}, year = {2021}, bdsk-file-1 = {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}} @incollection{BacutaChenXu2013Equidistribution, author = {Bacuta, C. and Chen, Long and Xu, J.}, booktitle = {Domain Decomposition Methods in Science and Engineering XX}, pages = {3--14}, series = {Lecture Notes in Computational Science and Engineering}, title = {Equidistribution and Optimal Approximation Class}, volume = {91}, year = {2013}} @incollection{Chen2010XZIdentity, author = {Chen, Long}, booktitle = {Domain Decomposition Methods in Science and Engineering XIX}, pages = {309--316}, title = {Deriving the X--Z Identity from Auxiliary Space Method}, year = {2010}} @incollection{ChenNochettoZhang2010MGObstacle2D, author = {Chen, Long and Nochetto, R. H. and Zhang, C.-S.}, booktitle = {Domain Decomposition Methods in Science and Engineering XIX}, pages = {229--236}, title = {Multigrid Methods for Elliptic Obstacle Problems on 2D Bisection Grids}, year = {2010}} @incollection{Chen2008ShortBisectionMATLAB, author = {Chen, Long}, booktitle = {Recent Advances in Computational Sciences -- Selected Papers from the International Workshop on Computational Sciences and Its Education}, editor = {Jorgensen, P. and Shen, X. and Shu, C.-W. and Yan, N.}, pages = {318--332}, title = {Short Implementation of Bisection in {MATLAB}}, year = {2008}} @incollection{ChenXu2005StreamlineDiffusionSingPert, author = {Chen, Long and Xu, J.}, booktitle = {Recent Advances in Adaptive Computation}, pages = {236--246}, publisher = {American Mathematical Society}, series = {Contemporary Mathematics}, title = {An Optimal Streamline Diffusion Finite Element Method for a Singularly Perturbed Problem}, volume = {383}, year = {2005}} @incollection{ChenSunXu2004MLHAFEM, author = {Chen, Long and Sun, P. and Xu, J.}, booktitle = {The Proceedings of the 15th Conference on Domain Decomposition Methods}, pages = {459--468}, publisher = {Springer}, series = {Lecture Notes in Computational Science and Engineering}, title = {Multilevel Homotopic Adaptive Finite Element Methods for Convection Dominated Problems}, volume = {40}, year = {2004}} @inproceedings{Chen2004MeshSmoothingODT, address = {Williamsburg, VA}, author = {Chen, Long}, booktitle = {Proceedings of the 13th International Meshing Roundtable}, organization = {Sandia National Laboratories}, pages = {109--120}, title = {Mesh Smoothing Schemes Based on Optimal Delaunay Triangulations}, year = {2004}} @incollection{ChenHuang2022DiscreteHessian3D, author = {Chen, Long and Huang, X.}, booktitle = {The Virtual Element Method and Its Applications}, doi = {10.1007/978-3-030-95319-5_3}, editor = {Antonietti, P. F. and Beir{\~a}o da Veiga, L. and Manzini, G.}, pages = {93--135}, publisher = {Springer}, series = {SEMA-SIMAI Springer Series}, title = {Discrete Hessian Complexes in Three Dimensions}, volume = {31}, year = {2022}, bdsk-url-1 = {https://doi.org/10.1007/978-3-030-95319-5_3}} @incollection{XuChenNochetto2009HgradHcurlHdivML, author = {Xu, J. and Chen, Long and Nochetto, R. H.}, booktitle = {Multiscale, Nonlinear and Adaptive Approximation}, editor = {DeVore, R. A. and Kunoth, A.}, publisher = {Springer}, title = {Optimal Multilevel Methods for $H(\mathrm{grad})$, $H(\mathrm{curl})$, and $H(\mathrm{div})$ Systems on Graded and Unstructured Grids}, year = {2009}} @incollection{ChenXu2007TopicsAFEM, address = {Beijing}, author = {Chen, Long and Xu, J.}, booktitle = {Adaptive Computations: Theory and Algorithms}, editor = {Tang, T. and Xu, J.}, pages = {1--31}, publisher = {Science Press}, title = {Topics on Adaptive Finite Element Methods}, year = {2007}} @unpublished{ChenWei2023AGSkewSplitting, author = {Chen, Long and Wei, J.}, note = {arXiv:2303.09009}, title = {Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations}, year = {2023}} @unpublished{ChenHuWu2020RandomizedFSD, author = {Chen, Long and Hu, X. and Wu, H.}, note = {arXiv:2006.06589}, title = {Randomized Fast Subspace Descent Methods}, year = {2020}} @unpublished{ChenHuang2020DivDivPreprint, author = {Chen, Long and Huang, X.}, note = {arXiv:2005.01271}, title = {Finite Elements for divdiv-Conforming Symmetric Tensors}, year = {2020}} @unpublished{ChenLuo2021StrongLyapunov, author = {Chen, Long and Luo, H.}, note = {arXiv:2108.00132}, title = {A Unified Convergence Analysis of First Order Convex Optimization Methods via Strong Lyapunov Functions}, year = {2021}} @unpublished{ChenHuang2021GeometricDecompSimplicial, author = {Chen, Long and Huang, X.}, note = {arXiv:2111.10712}, title = {Geometric Decompositions of the Simplicial Lattice and Smooth Finite Elements in Arbitrary Dimension}, year = {2021}} @unpublished{ChenLuo2019HessianDrivenNAG, author = {Chen, Long and Luo, H.}, note = {arXiv:1912.09276}, title = {First Order Optimization Methods Based on Hessian-Driven Nesterov Accelerated Gradient Flow}, year = {2019}} @techreport{Chen2008iFEM, author = {Chen, Long}, institution = {University of California at Irvine}, note = {Technical Report}, title = {{$i$FEM}: An Integrated Finite Element Methods Package in {MATLAB}}, year = {2008}} @techreport{ChenZhang2006AFEMMatlab, author = {Chen, Long and Zhang, C.-S.}, institution = {University of Maryland}, note = {Technical Report}, title = {AFEM@matlab: A {MATLAB} Package of Adaptive Finite Element Methods}, year = {2006}} @phdthesis{Chen2005PhD, author = {Chen, Long}, school = {The Pennsylvania State University}, title = {Robust and Accurate Algorithms for Solving Anisotropic Singularities}, year = {2005}} @comment{BibDesk Static Groups{ group name Fast Solvers keys ChenGuoWeiZou2025PrecondNonlinearPDE,ChenGuoWei2025TPDVarPrecond group name Finite element complexes keys ChenHuang2025ComplexesFromComplexes,ChenHuang2025DivDivBiharmonic,ChenHuang2018HelmholtzDecoupling,ChenHuHuang2018HHJMultigrid,ChenHuang2021DivDiv3D,ChenHuang2022ElasticityComplex3D,ChenHuang2022DiscreteHessian3D,ChenHuang2024DeRhamStokes3D,ChenHuang2024HdivTensorsConstraints,ChenHuang2024FEMComplexes2DChinese,ChenHuangZhangZhao2025StokesSuperconv,ChenHuangZhang2025DistCurlDivQuadCurl group name Finite element tensor calculus keys ChenChenGaoHuangWei2025SmoothSpaces,ChenHuang2025HybridizableStress,ChenHuang2025ComplexesFromComplexes,ChenHuang2025DivDivBiharmonic,ChenHuangZhang2025DistCurlDivQuadCurl,ChenHuangZhangZhao2025StokesSuperconv,ChenChenHuangWei2024GeoDecompFaceEdge,ChenHuang2024TangentNormalForms,ChenHuang2024HdivTensorsConstraints,ChenHuang2024FEMComplexes2DChinese,ChenHuang2024DeRhamStokes3D,ChenHuang2022DivDivArbitraryDim,ChenHuang2022ElasticityComplex3D,ChenHuang2022DiscreteHessian3D,ChenHuang2021DivDiv3D,ChenHuang2021GeometricDecompSimplicial,ChenHuang2020NonconfVEM2mRn,ChenHuang2020DivDivPreprint,ChenHuHuang2018HHJMultigrid,ChenHuHuang2018FASPLinearElasticity,ChenHuHuangMan2018ResidualElasticity,ChenHuang2018HelmholtzDecoupling,ChenHuHuang2016StabilizedMixedElasticity group name Machine Learning keys GuoCaoChen2023TransformerBVP,NguyenSuliafuOsherChenWang2021FMMformer group name Mesh keys group name Numerical PDEs keys ChenHuangParkWang2025PrimalSDGPolytopal,CaoChenHuang2022QuadCurlError group name Optimization keys ChenXuWeiLuoYao2025AMDSplitting,WeiChen2025AORHB,ChenLuoWei2025AGMSplitting,ChenXu2025HNAGpp }}