publication

Paper Submitted

  1. L. Chen and J. Wei. Accelerated Gradient and Skew-Symmetric Splitting Methods for a Class of Monotone Operator Equations. Submitted. 2024.
  2. S. Cao, L. Chen, and S. Lee. Edge-averaged virtual element methods for convection-diffusion and convection-dominated problems. Submitted, 2024.
  3. L. Chen and X. Huang. H(div)-conforming Finite Element Tensors. Submitted, 2024.
  4. L. Chen, R. Guo, and J. Wei. Transformed Primal-Dual Methods with Variable-Preconditioners. Submitted. 2023.
  5. L. Chen, X. Huang, and C. Zhang. Distributional Finite Element curl div Complexes and Application to Quad Curl Problems. Submitted. 2023.
  6. L. Chen and X. Huang. Complexes from Complexes: Finite Element Complexes in Three Dimensions. Submitted, 2023.
  7. L. Chen and X. Huang. Finite Element Complexes in Two Dimensions. Submitted, 2023.

Paper Published/Accepted

  1. C.Y. Chen, L. Chen, X.H. Huang, and H.Y. Wei. Geometric Decomposition and Efficient Implementation of High Order Face and Edge Elements. Communications in Computational Physics. 2024.
  2. L. Chen and X. Huang. A New Div-Div-Conforming Symmetric Tensor Finite Element Space with Applications to the Biharmonic Equation. Mathematics of Computation. 2024.
  3. L. Chen, R. Guo, and J. Zou. A Family of Immersed Finite Element Spaces and Applications to Three Dimensional H(curl) Interface Problems. SIAM Journal on Scientific Computing, 2023.
  4. L. Chen and X. Huang. Finite Element de Rham and Stokes Complexes in Three Dimensions. Mathematics of Computation, 2023.
  5. S. Kia, J. Wei, and L. Chen. Distributed Optimal Resource Allocation Using Transformed Primal-Dual Method. 2023 American Control Conference (ACC).
  6. Y. Xie, S. Cao, L. Chen, and L. Zhong. Convergence and Optimality of an adaptive modified weak Galerkin finite element method. Numerical Methods for Partial Differential Equations, 2023.
  7. R. Guo, S. Cao, and L. Chen. Transformer Meets Boundary Value Inverse Problem. ICLR, 2023.
  8. L. Chen and J. Wei. Transformed Primal-Dual Methods for Nonlinear Saddle Point Systems. Journal of Numerical Mathematics. 2023.
  9. S. Cao, L. Chen, and R. Guo. Immersed Virtual Element Methods for Electromagnetic Interface Problems in Three Dimensions. Mathematical Models and Methods in Applied Sciences. 2023.
  10. S. Cao, L. Chen, R. Guo, and F. Lin. Immersed Virtual Element Methods for Elliptic Interface Problems in Two Dimensions. Journal of Scientific Computing, 93 (12), 2022.
  11. L. Chen and X. Huang. Finite elements for div and divdiv conforming symmetric tensors in arbitrary dimensions. SIAM Journal on Numerical Analysis, 60: 1932-1961, 2022.
  12. D. Wang, B. Zheng, L. Chen, G. Lin and J. Xu. Block Triangular Preconditioning for Stochastic Galerkin Method. Journal of Computational and Applied Mathematics. 412,114298, 2022.
  13. L. Chen and X. Huang. A Finite element elasticity complex in three dimensions. Mathematics of Computation. 91, 2095–2127, 2022.
  14. S. Cao, L. Chen, and X. Huang. Error analysis of a decoupled finite element method for quad-curl problems. Journal of Scientific Computing, 90(29) 2022.
  15. T.M. Nguyen, V. Suliafu, S.J. Osher, L. Chen, and B. Wang. FMMformer: Efficient and Flexible Transformer via Decomposed Near-field and Far-field Attention. NeurIPS. 2021.
  16. H. Luo and L. Chen. From Differential Equation Solvers to Accelerated First-Order Methods for Convex Optimization. Mathematical Programming. 195, 735–781, 2021.
  17. L. Chen and X. Huang. Finite elements for divdiv-conforming symmetric tensors in three dimensions. Mathematics of Computation. 91, 1107–1142, 2021.
  18. S. Cao, L. Chen, and R. Guo. A Virtual Finite Element Method for Two Dimensional Maxwell Interface Problems with a Background Unfitted Mesh. Mathematical Models and Methods in Applied Sciences, 31(14), 2907–2936, 2021.
  19. L. Chen and X. Huang. Discrete Hessian complexes in three dimensions. In “The Virtual Element Method ad its Applications”. SEMA-SIMAI Springer series. 2021.
  20. L. Chen, X. Hu, and S. Wise. Convergence Analysis of the Fast Subspace Descent Methods for Convex Optimization Problems. Mathematics of Computation. 2249-2282, 89, 2020.
  21. L. Chen and X. Huang. Nonconforming Virtual Element Method for 2m-th Order Partial Differential Equations in R^n. Mathematics of Computation. 89, 1711-1744, 2020.
  22. S. Cao and L. Chen. Anisotropic Error Estimates of The Linear Nonconforming Virtual Element Methods. SIAM Journal on Numerical Analysis. 57(3): 1058-1081, 2019.
  23. G. Wang, F. Wang, L. Chen, and Y. He. A Divergence Free Weak Virtual Element Method for the Stokes-Darcy Problem on General Meshes. Computer Methods in Applied Mechanics and Engineering. 344: 998-1020, 2019.
  24. L. Chen and F. Wang. A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polyhedral Meshes. Journal of Scientific Computing. 78(2), 864-886, 2019.
  25. L. Chen and X. Huang. Decoupling of Mixed Methods Based on Generalized Helmholtz Decompositions. SIAM Journal on Numerical Analysis. 56(5):2796-2825, 2018.
  26. S. Cao and L. Chen. Anisotropic Error Estimates of The Linear Virtual Element Method on Polygonal Meshes. SIAM Journal on Numerical Analysis. 56(5):2913-2939, 2018.
  27. L. Chen, J. Hu, X. Huang. Multigrid Methods for Hellan-Herrmann-Jonson Mixed Method of Kirchhoff Plate Bending Problems. Journal of Scientific Computing 76:673, 2018. https://doi.org/10.1007/s10915-017-0636-z
  28. L. Chen and J. Huang. Some Error Analysis on Virtual Element Methods. Calcolo. 55:5,2018.
  29. L. Chen, Y. Wu, L. Zhong and J. Zhou. Multigrid Preconditioners for Mixed Finite Element Methods of Vector Laplacian. Journal of Scientific Computing, 77(1):101--128, Oct. 2018.
  30. L. Chen, J. Hu, X. Huang, and H. Man. Residual-Based A Posteriori Error Estimates for Symmetric Conforming Mixed Finite Elements for Linear Elasticity Problems. Science China Mathematics. 2017.
  31. L. Chen and Y. Wu. Convergence of Adaptive Mixed Finite Element Methods for Hodge Laplacian Equation without harmonic forms. SIAM Journal on Numerical Analysis. 55(6), 2905–2929, 2017.
  32. J. Huang, L. Chen and H. Rui. Multigrid Methods for A Mixed Finite Element Method of The Darcy-Forchheimer Model. Journal of Scientific Computing, 74(1), 396–411, 2017.
  33. L. Chen, J. Hu, X. Huang. Fast Auxiliary Space Preconditioner for Linear Elasticity in Mixed Form. Mathematics of Computation. 87(312):1601--1633, 2018.
  34. L. Chen, H. Wei, M. Wen. An Interface-Fitted Mesh Generator and Virtual Element Methods for Elliptic Interface Problems. Journal of Computational Physics. 334(1), 2017, 327–348. http://dx.doi.org/10.1016/j.jcp.2017.01.004
  35. L. Chen, J. Hu, X. Huang. Stabilized mixed finite element methods for linear elasticity on simplicial grids in R^n. Comput. Methods Appl. Math. 17(1): 17-31, 2017.
  36. B. Zheng, L.P. Chen, X. Hu, L. Chen, R.H. Nochetto, J. Xu. Fast multilevel solvers for a class of discrete fourth order parabolic problems. Journal of Scientific Computing, 2016. DOI 10.1007/s10915-016-0189-6
  37. W. Wang, L. Chen, and J. Zhou. Postprocessing mixed finite element methods for solving Cahn-Hilliard equation: Methods and Error Analysis. Journal of Scientific Computing, 67(2), 724-746, 2016. DOI 10.1007/s10915-015-0101-9
  38. L. Chen, R.H. Nochetto, E. Otarola, A.J. Salgado. Multilevel methods for nonuniformly elliptic operators and Fractional Diffusion. Mathematics of Computation, 85, 2583-2607, 2016. doi:10.1090/mcom/3089
  39. L. Chen. Multi-Grid Methods for Saddle Point Systems using Constrained Smoothers. Computers and Mathematics with Applications, 70(12) 2854–2866, 2015.doi:10.1016/j.camwa.2015.09.020
  40. L. Chen, J. Wang, Y. Wang and X. Ye. Au Auxiliary Space Multigrid Preconditioner for the Weak Galerkin Method. Computers and Mathematics with Applications, 70(4):330–344 2015. doi:10.1016/j.camwa.2015.04.016
  41. P. Zu, L. Chen, and J. Xin. A Computational Study of Residual KPP Front Speeds in Time-Periodic Cellular Flows in the Small Diffusion Limit. Physica D: Nonlinear Phenomena, 311, 37 - 44, 2015. doi:10.1016/j.physd.2015.07.001
  42. L. Chen, R.H. Nochetto, E. Otarola, A.J. Salgado. A PDE approach to fractional diffusion: a posteriori error analysis. Journal of Computational Physics, 293, 339-358, 2015. DOI: 10.1016/j.jcp.2015.01.001
  43. L. Chen, X. Hu, M. Wang, and J. Xu. A Multigrid Solver based on Distributive Smoother and Defect Correction for Oseen Problems. Numerical Mathematics: Theory, Methods and Applications, 8(2), 237-252, 2015. doi: 10.4208/nmtma.2015.w09si
  44. L. Chen. A simple construction of a Fortin operator for the two dimensional Taylor-Hood element. Computers and Mathematics with Applications, 68(10),1368–1373, 2014. DOI: 10.1016/j.camwa.2014.09.003
  45. L. Chen, M. Wang, and L. Zhong. Convergence Analysis of The Triangular MAC Scheme for Stokes Equations. Journal of Scientific Computing, 63(3), 716-744, 2015. (DOI) 10.1007/s10915-014-9916-z
  46. J. Zhou, L. Chen, Y. Huang and W. Wang. An Efficient Two-Grid Scheme for the Cahn-Hillard Equation. Communications in Computational Physics, 17(01), 127-145, 2015. DOI: doi:10.4208/cicp.231213.100714a
  47. J. Hateley, H. Wei and L. Chen. Fast Methods for Computing Centroidal Voronoi Tessellations. Journal of Scientific Computing, 63(1), 185-212, 2015, (DOI) 10.1007/s10915-014-9894-1.
  48. J. Zhou, X. Hu, L. Zhong, S. Shu, and L. Chen. Two-Grid Methods for Maxwell Eigenvalue Problems. SIAM Journal on Numerical Analysis, 52(4), 2027--2047, 2014.
  49. H. Wei, L. Chen, Y. Huang and B. Zheng. Adaptive Mesh Refinement and Superconvergence for Two Dimensional Interface Problems. SIAM Journal on Scientific Computing, 36(4), A1478--A1499, 2014.
  50. L. Chen, J. Wang and X. Ye. A posteriori error estimates for Weak Galerkin finite element methods for second order elliptic problems. Journal of Scientific Computing, 59(2), 496-511, 2014.
  51. Y. Wu, X. Xie, and L. Chen. Hybrid Stress Finite Volume Method for Linear Elasticity Problems. International Journal of Numerical Analysis and Modeling, 10(3), 634–656, 2013.
  52. L. Chen and M. Wang. Cell conservative flux recovery and a posteriori error estimate of vertex-centered finite volume methods. Advances in Applied Mathematics and Mechanics, 5 (5), 705-727. 2013.
  53. M. Wang and L. Chen. Multigrid Methods for the Stokes equations using Distributive Gauss-Seidel Relaxations based on the Least Squares Commutator. Journal of Scientific Computing. 56(2): 409-431, 2013. (DOI) 10.1007/s10915-013-9684-1
  54. L. Chen, M.J. Holst, J. Xu, and Y. Zhu. Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids. Computing and Visualization in Science, 15(5), 271--289, 2012.
  55. W. C. Lo, L. Chen, M. Wang, and Q. Nie. A Robust and Efficient Method for Steady State Patterns in Reaction-Diffusion Systems. Journal of Computational Physics, 231(15), 5062-5077, 2012.
  56. Y. Wu, L. Chen, X. Xie, and J. Xu. Convergence Analysis of V-Cycle Multigrid Methods for Anisotropic Elliptic Equations. IMA Journal of Numerical Analysis, IMA Journal of Numerical Analysis 32(4):1329–1347, 2012; doi: 10.1093/imanum/drr043.
  57. L. Zhong, L. Chen, S. Shu, G. Wittum, and J. Xu. Quasi-optimal convergence of adaptive edge finite element methods for three dimensional indefinite time-harmonic Maxwell's equations. Mathematics of Computation. 81(278):623-642, 2012.
  58. L. Chen, R.H. Nochetto and J. Xu. Optimal Multilevel Methods for Graded Bisection Grids. Numerische Mathematik. 120(1): 1-34, 2011.
  59. L. Chen and M.J. Holst. Efficient Mesh Optimization Schemes based on Optimal Delaunay Triangulations. Computer Methods in Applied Mechanics and Engineering 200, 967–984, 2011.
  60. H. We, L. Chen and Y. Huang. Superconvergence and Gradient Recovery of Linear Finite Elements for the Laplace-Beltrami Operator on General Surfaces. SIAM Journal on Numerical Analysis, 48(5):1920-1943, 2010.
  61. L. Chen and C-S. Zhang. A coarsening algorithm on adaptive grids by newest vertex bisection and its applications. Journal of Computational Mathematics, 28(6):767-789, 2010.
  62. L. Zhong, S. Shu, L. Chen, and J. Xu. Convergence of adaptive edge finite element methods for H(curl)-elliptic problems. Numerical Linear Algebra with Applications. 17(2-3):415-432, 2010.
  63. P. Sun, L. Chen, and J. Xu. Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. 43(1), 24-43. Journal of Scientific Computing. 2010.
  64. L. Chen. A New Class of High Order Finite Volume Methods for Second Order Elliptic equations. 47(6), 4021-4043. SIAM Journal on Numerical Analysis. 2010.
  65. L. Chen and H. Li. Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities. Journal of Computational Mathematics. 28, 11-31, 2010.
  66. L. Chen. On minimizing the linear interpolation error of convex quadratic functions and the optimal simplex. East Journal on Approximations, 14(3), 271--284, 2008.
  67. L. Chen, M.J. Holst, and J. Xu. Convergence and optimality of adaptive mixed finite element methods. 78: 35--53, Mathematics of Computation, 2009.
  68. L. Chen and J. Xu. Stability and accuracy of adapted finite element methods for singularly perturbed problems. Numerische Mathematik, 109(2): 167 - 191, 2008.
  69. L. Chen, Y. Wang and J. Wu. Stability of a Streamline Diffusion Finite Element Methods for Turning Point Problems. Journal of Computational and Applied Mathematics, 220, 712 - 724, 2008.
  70. L. Chen, M.J. Holst, and J. Xu. The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation. SIAM Journal on Numerical Analysis, 45(6): 2298-2320, 2007.
  71. J. Jiang, S. Shu, Y. Huang, and L. Chen. A mesh adaptive method for two-dimensional three-tempeature heat conduction equations. Chinese Journal of Computational Physics, 24(1):19-28, 2007.
  72. L. Chen, P. Sun, and J. Xu. Optimal anisotropic simplicial meshes for minimizing interpolation errors in $L^p$ norm. Mathematics of Computation, 76(257):179-204, 2007.
  73. L. Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3(3):273-282, 2006.
  74. L. Chen. New analysis of the sphere covering problems and optimal polytope approximation of convex bodies. Journal of Approximation Theory, 133(1):134-145, 2005.
  75. L. Chen and J. Xu. Optimal Delaunay triangulations. Journal of Computational Mathematics, 22(2):299-308, 2004.

Conference Proceedings

  1. C. Bacuta, L. Chen and J. Xu. Equidistribution and optimal approximation class. Domain Decomposition Methods in Science and Engineering 20. 2013.
  2. L. Chen. Deriving the X-Z Identity from Auxiliary Space Method. Domain Decomposition Methods in Science and Engineering XIX, 309-316, 2010.
  3. L. Chen, R.H. Nochetto and C-S. Zhang. Multigrid Methods for Elliptic Obstacle Problems on 2D Bisection Grids. Domain Decomposition Methods in Science and Engineering XIX, 229-236, 2010.
  4. L. Chen. Short bisection implementation in MATLAB. In Recent Advances in Computational Sciences -- Selected Papers from the International Workship on Computational Sciences and Its Education, 318 -- 332, 2008
  5. L. Chen and J. Xu. An optimal streamline diffusion finite element method for a singularly perturbed problem. In AMS Contemporary Mathematics Series: Recent Advances in Adaptive Computation, volume 383, pages 236-246, Hangzhou, 2005.
  6. L. Chen, P. Sun, and J. Xu. Multilevel homotopic adaptive finite element methods for convection dominated problems. In The Proceedings for 15th Conferences for Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering 40, pages 459-468. Springer, 2004.
  7. L. Chen. Mesh smoothing schemes based on optimal Delaunay triangulations. In 13th International Meshing Roundtable, pages 109-120, Williamsburg, VA, 2004. Sandia National Laboratories.

Monograph

  1. L. Chen. Robust and Accurate Algorithms for Solving Anisotropic Singularities. PhD thesis, Department of Mathematics, The Pennsylvania State University, 2005.
  2. L. Chen and J. Xu. Topics on adaptive finite element methods. Book Chapter in Adaptive Methods: Theory and algorithm, 2007.
  3. J. Xu, L. Chen, and R.H. Nochetto. Optimal Multilevel Methods for H(grad), H(curl), and H(div) Systems on Graded and Unstructured Grids. Ronald A. DeVore, Angela Kunoth (Eds.), Springer, 2009.

Others

  1. L. Chen. iFEM: an integrated finite element methods package in MATLAB. Technical Report, University of California at Irvine. 2009.
  2. L. Chen and C-S. Zhang. AFEM@matlab: a MATLAB package of Adaptive Finite Element Methods. Technical Report. University of Maryland. 2006.
  3. L. Chen, X. Hu, and H. Wu. Randomized Fast Subspace Descent Methods. 2020.
  4. L. Chen and X. Huang. Finite elements for divdiv-conforming symmetric tensors. 2020.
  5. L. Chen and H. Luo. A Unified Convergence Analysis of First Order Convex Optimization Methods via Strong Lyapunov Functions. Submitted. 2021.
  6. L. Chen and X. Huang. Geometric decompositions of the simplicial lattice and smooth finite elements in arbitrary dimension. 2021.

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