Dr Stefano Giani stefano.giani@durham.ac.uk
Associate Professor
An A Posteriori Error Estimator for Hp-Adaptive Discontinuous Galerkin Methods for Elliptic Eigenvalue Problems
Giani, S.; Hall, E.
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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Copyright Statement
Electronic version of an article published as Mathematical models and methods in applied sciences, 22, 10, 2012, 1250030, DOI: 10.1142/S0218202512500303 © copyright World Scientific Publishing Company http://www.worldscientific.com/worldscinet/m3as
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