publication
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Paper Submitted
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Paper Published/Accepted
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Monograph
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Others
Paper Submitted
- L. Chen, J. Xu and Y. Zhu. Local Multilevel Preconditioners for
Elliptic Equations with Jump Coefficients on Bisection Grids. To be
submitted, 2009.
- L. Chen. Optimal Rate of Convergence in $L^2$-Norm of An Adaptive Finite Element Method for Elliptic Equations. Submitted,2009.
- L. Chen, R.H. Nochetto and J. Xu. Local Multilevel Methods on Graded Bisection Grids. To be submitted, 2009.
- L. Chen. Some First and Second Order Finite Volume Methods for the Stokes Problem. Submitted,2009.
- 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. Submitted, 2009.
- L. Chen. iFEM: an innovative finite element methods package in MATLAB. Submitted,2009.
- L. Chen and C-S. Zhang. A coarsening algorithm on adaptive grids by newest vertex bisection and its applications. Submitted,2009.
Paper Published/Accepted
- L. Zhong, S. Shu, L. Chen, and
J. Xu. Convergence of adaptive edge finite element methods for H(curl)-elliptic problems. Accepted
by Numerical Linear Algebra with Applications, 2009.
- P. Sun, L. Chen, and
J. Xu. Numerical studies of adaptive finite element methods for two dimensional convection-dominated problems. Accepted
by Journal of Scientific Computing. 2009.
- L. Chen. A New Class of High Order Finite Volume Methods for Second Order Elliptic equations. Accepted
by SIAM Journal on Numerical Analysis. 2009.
- L. Chen and
H. Li. Superconvergence of Gradient Recovery Schemes on graded meshes for corner singularities. Journal
of Computational Mathematics. 28, 11-31, 2010.
- 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
- 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. 78:
35--53, Mathematics of
Computation, 2009.
- 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.
- 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
- L. Chen and C-S. Zhang. AFEM@matlab: a MATLAB package of Adaptive
Finite Element Methods. Technical Report. University of
Maryland. 2006.