Gudi, Thirupathi and Guzman, Johnny (2014) CONVERGENCE ANALYSIS OF THE LOWEST ORDER WEAKLY PENALIZED ADAPTIVE DISCONTINUOUS GALERKIN METHODS. In: ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 48 (3). pp. 753-764.
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In this article, we prove convergence of the weakly penalized adaptive discontinuous Galerkin methods. Unlike other works, we derive the contraction property for various discontinuous Galerkin methods only assuming the stabilizing parameters are large enough to stabilize the method. A central idea in the analysis is to construct an auxiliary solution from the discontinuous Galerkin solution by a simple post processing. Based on the auxiliary solution, we define the adaptive algorithm which guides to the convergence of adaptive discontinuous Galerkin methods.
| Item Type: | Journal Article |
|---|---|
| Publication: | ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE |
| Publisher: | EDP SCIENCES S A |
| Additional Information: | copyright for this article belongs to EDP SCIENCES S A, FRANCE. |
| Keywords: | Contraction; adaptive finite element; discontinuous Galerkin |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 12 Jun 2014 09:55 |
| Last Modified: | 12 Jun 2014 09:55 |
| URI: | http://eprints.iisc.ac.in/id/eprint/49165 |
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