publication
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Paper in Prepration
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Preprint
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Paper Submitted
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Paper Published/Accepted
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Monograph
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Others
Paper in Prepration
- L. Chen. iFEM: an innovative finite element methods package in MATLAB, 2008.
- L. Chen, P. Sun and J. Xu. Numerical Study of Finite Element Methods for 2D Convection-Dominated Convection-Diffusion Problems. In prepration, 2008.
Preprint
- L. Chen and M.J. Holst. Efficient Mesh Optimization Schemes based on Optimal Delaunay Triangulations. Preprint, 2008.
- L. Chen, R.H. Nochetto and J. Xu. Multilevel methods on graded bisection grids II: H(curl) and H(div) systems. Preprint. 2008.
- L. Chen, R.H. Nochetto and
J. Xu. Multilevel methods on graded bisection grids I: H1 system. To be submitted. 2007.
Paper Submitted
- L. Chen. A New Class of High Order Finite Volume Methods for Second Order Elliptic equations. Submitted. 2008.
- L. Chen and C-S. Zhang. A coarsening algorithm and multilevel methods on adaptive grids by newest vertex bisection. Submitted, 2007.
Paper Published/Accepted
- L. Chen and H. Li. Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities. Accepted by Journal of Computational Mathematics. 2008.
- 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.
- L. Chen, M.J. Holst, and
J. Xu. Convergence and optimality of adaptive mixed finite element methods. Article electronically published on June 30, 2008, Mathematics of Computation, 2008.
- L. Chen and
J. Xu. Stability and accuracy of adapted finite element methods for singularly perturbed problems. Numerische Mathematik, 109(2): 167 - 191, 2008.
- 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.
- 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.
- 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.
- 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.
- L. Chen. Superconvergence of tetrahedral linear finite elements. International
Journal of Numerical Analysis and Modeling, 3(3):273-282, 2006.
- 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.
- 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.
- 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.
- L. Chen. Mesh smoothing schemes based on optimal Delaunay triangulations. In
13th International Meshing Roundtable, pages 109-120,
Williamsburg, VA, 2004. Sandia National Laboratories.
- L. Chen and J. Xu. Optimal Delaunay triangulations. Journal of
Computational Mathematics, 22(2):299-308, 2004.
Monograph
- L. Chen. Robust and Accurate Algorithms for Solving Anisotropic Singularities. PhD thesis, Department of Mathematics, The
Pennsylvania State University, 2005.
- L. Chen and J. Xu. Topics on adaptive finite element methods. Book
Chapter in Adaptive Methods: Theory and algorithm, 2007.
Others
- L. Chen. Short bisection implementation in MATLAB. Research Notes, 2006
- L. Chen and C-S. Zhang. AFEM@matlab: a MATLAB package of Adaptive
Finite Element Methods. Technical Report. University of
Maryland. 2006.