publication

Paper Submitted

  1. L. Chen and F. Wang. A Divergence Free Weak Virtual Element Method for the Stokes Problem on Polyhedral Meshes. Submitted. 2017.
  2. L. Chen and J. Huang. Some Error Analysis on Virtual Element Methods. Submitted. 2017.
  3. L. Chen and X. Huang. Differential Complexes, Helmholtz Decompositions, and Decoupling of Mixed Methods. Submitted. 2017.
  4. L. Chen, Y. Wu, L. Zhong and J. Zhou. Multigrid Preconditioners for Mixed Finite Element Methods of Vector Laplacian. Submitted. 2015.
  5. L. Chen, J. Hu, X. Huang. Multigrid Methods for Hellan-Herrmann-Jonson Mixed Method of Kirchhoff Plate Bending Problems. Submitted, 2015.
  6. L. Chen. Multigrid Methods for Constrained Minimization Problems and Application to Saddle Point Problems. Submitted,2014.

Paper Published/Accepted

  1. 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.
  2. L. Chen and Y. Wu. Convergence of Adaptive Mixed Finite Element Methods for Hodge Laplacian Equation without harmonic forms. SIAM Journal on Numerical Analysis. 2017.
  3. J. Huang, L. Chen and H. Rui. Multigrid Methods for A Mixed Finite Element Method of The Darcy-Forchheimer Model. Journal of Scientific Computing, 2017.
  4. L. Chen, J. Hu, X. Huang. Fast Auxiliary Space Preconditioner for Linear Elasticity in Mixed Form. Mathematics of Computation. 2017.
  5. 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
  6. L. Chen, J. Hu, X. Huang. Stabilized mixed finite element methods for linear elasticity on simplicial grids in R^n. Comput. Methods Appl. Math. 2016.
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  23. 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.
  24. 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
  25. 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.
  26. 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.
  27. 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.
  28. 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.
  29. L. Chen, R.H. Nochetto and J. Xu. Optimal Multilevel Methods for Graded Bisection Grids. Numerische Mathematik. 120(1): 1-34, 2011.
  30. 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.
  31. H. Wei, 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.
  32. 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.
  33. 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.
  34. 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.
  35. 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.
  36. L. Chen and H. Li. Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities. Journal of Computational Mathematics. 28, 11-31, 2010.
  37. 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.
  38. L. Chen, M.J. Holst, and J. Xu. Convergence and optimality of adaptive mixed finite element methods. 78: 35--53, Mathematics of Computation, 2009.
  39. L. Chen and J. Xu. Stability and accuracy of adapted finite element methods for singularly perturbed problems. Numerische Mathematik, 109(2): 167 - 191, 2008.
  40. 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.
  41. 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.
  42. 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.
  43. 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.
  44. L. Chen. Superconvergence of tetrahedral linear finite elements. International Journal of Numerical Analysis and Modeling, 3(3):273-282, 2006.
  45. 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.
  46. 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.