Research News

Software: LNG_FEM, a software package for generating graded meshes and solving elliptic PDEs with singular solutions in arbitrary 2-D domains for different boundary conditions, 08/2007

An update of my research on conner-like singularities, the finite element method (FEM), and the multigrid method (MG): The Finite Element Method on Domains with Conical or Angular Points, 6th International Congress on Industrial & Applied Mathematics, Zürich, Switzland, 07/2007

A graphic introduction for my research: Finite Element Method on Polygonal Domains with Applications on Degenerate PDEs, Third Place of the Poster Competition, Computation Day, Penn State University, 02/2006

Movies: Graded Meshes for Elliptic Equations with Singularities

List of publications / preprints:
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1. J. Brannick, H. Li and L. Zikatanov, Uniform convergence of the multigrid V-cycle on graded meshes for corner singularities (PDF), Numerical Linear Algebra with Applications (15:291–306, DOI: 10.1002/nla.574), 2008

2. H. Li and V. Nistor, Analysis of a modified Schroedinger operator in 2D: regularity, index, and FEM (PDF), Journal of Computational and Applied Mathematics, (DOI: 10.1016/j.cam.2008.05.009), 2008

3. H. Li, A-priori analysis and the finite element method for a class of degenerate elliptic equations (PDF), to appear in Mathematics of Computation, 2008

4. L. Chen and H. Li, Superconvergence of gradient recovery schemes on graded meshes for corner singularities (PDF), submitted for publication, 01/2008

5. H. Li, A. Mazzucato, and V. Nistor, On the analysis of the Finite Element Method on general polygonal domains I: transmission problems and a priori estimates (PDF), CCMA preprint AM319, submitted for publication, 09/2007

6. H. Li, Uniform convergence of the multigrid V-cycle on graded meshes (PDF), Proceedings of the Thirteenth Copper Mountain Conference on Multigrid Methods, 2007

7. H. Li and V. Nistor, LNG_FEM: Generating graded meshes and solving elliptic equations on 2-D domains of polygonal structures (PDF), IMA preprint 2172, 08/2007