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

Giani, S.; Hall, E.

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: Apr 20, 2015
• 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