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An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems

Giani, S.; Hall, E.

An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems Thumbnail


Authors

E. Hall



Abstract

In this paper we present a residual-based a posteriori error estimator for hp-adaptive discontinuous Galerkin methods for elliptic eigenvalue problems. In particular, we use as a model problem the Laplace eigenvalue problem on bounded domains in ℝd, 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 also for non-convex domains 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.

Citation

Giani, S., & Hall, E. (2012). An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems. Mathematical Models and Methods in Applied Sciences, 22(10), https://doi.org/10.1142/s0218202512500303

Journal Article Type Article
Publication Date Oct 1, 2012
Deposit Date Feb 12, 2013
Publicly Available Date Mar 28, 2024
Journal Mathematical Models and Methods in Applied Sciences
Print ISSN 0218-2025
Electronic ISSN 1793-6314
Publisher World Scientific Publishing
Peer Reviewed Peer Reviewed
Volume 22
Issue 10
DOI https://doi.org/10.1142/s0218202512500303
Keywords Discontinuous Galerkin methods, Elliptic eigenvalue problems, a posteriori error estimation, hp-adaptivity.
Related Public URLs http://eprints.nottingham.ac.uk/1498/1/giania_hall_preprint.pdf

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