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An analysis of discontinuous Galerkin methods for elliptic problems |
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| Authors: | Reinhold Schneider Yuesheng Xu Aihui Zhou |
| Institution: | 001. Fakult?t für Mathematik, Technische Universit?t Chemnitz, D-09107, Chemnitz, Germany 002. Department of Mathematics, Syracuse University, Syracuse, NY, 13244, USA, Beijing, 100080, P. R. China 003. Institute of Computational Mathematics, and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O. Box 2719, Beijing, 100080, P. R. China |
| Abstract: | We study global and local behaviors for three kinds of discontinuous Galerkin schemes for elliptic equations of second order. We particularly investigate several a posteriori error estimations for the discontinuous Galerkin schemes. These theoretical results are applied to develop local/parallel and adaptive finite element methods, based on the discontinuous Galerkin methods. Dedicated to Dr. Charles A. Micchelli on the occasion of his 60th birthday with friendship and esteem Mathematics subject classifications (2000) 65N12, 65N15, 65N30. Aihui Zhou: Subsidized by the Special Funds for Major State Basic Research Projects, and also partially supported by National Science Foundation of China. Reinhold Schneider: Supported in part by DFG Sonderforschungsbereich SFB 393. Yuesheng Xu: Correspondence author. Supported in part by the US National Science Foundation under grants DMS-9973427 and CCR-0312113, by Natural Science Foundation of China under grant 10371122 and by the Chinese Academy of Sciences under program “Hundreds Distinguished Young Chinese Scientists”. |
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