## An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems

Giani, Stefano and Hall, Edward (2011) An a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. Mathematical Models and Methods in Applied Sciences (M3AS), 22 (10). p. 1299001. ISSN 0218-2025 (Submitted)

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## Abstract

In this paper we present a residual-based {\em a posteriori} error estimator for $hp$-adaptive discontinuous Galerkin (DG) methods for elliptic eigenvalue problems. In particular we use as a model problem the Laplace eigenvalue problem on bounded domains in $\mathbb{R}^d$, $d=2,3$, with homogeneous Dirichlet boundary conditions. Analogous error estimators can be easily obtained for more complicated elliptic eigenvalue problems. We prove the reliability and efficiency of the residual based error estimator and use numerical experiments to show that, under an $hp$-adaptation strategy driven by the error estimator, exponential convergence can be achieved, even for non--smooth eigenfunctions.

Item Type: Article Preprint of an article submitted for consideration in Mathematical Models and Methods in Applied Sciences (M3AS) © 2011 copyright World Scientific Publishing Company. http://www.worldscinet.com/m3as/m3as.shtml Faculty of Science > School of Mathematical Sciences 1498 Hall, Dr Edward 15 Aug 2011 09:00 15 May 2013 14:36

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