Convergence analysis of the lowest order weakly penalized adaptive discontinuous Galerkin methods
1 Department of Mathematics, Indian Institute of Science, 56002
2 Division of Applied Mathematics, Brown University, Providence, 02912 RI, USA.
Revised: 3 June 2013
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.
Mathematics Subject Classification: 65N30 / 65N15
Key words: Contraction / adaptive finite element / discontinuous Galerkin
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