Giani, S. and 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). p. 1250030.
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.
|Keywords:||Discontinuous Galerkin methods, Elliptic eigenvalue problems, a posteriori error estimation, hp-adaptivity.|
|Full text:||(AM) Accepted Manuscript|
Download PDF (382Kb)
|Publisher Web site:||http://dx.doi.org/10.1142/S0218202512500303|
|Publisher 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|
|Record Created:||20 Apr 2015 12:05|
|Last Modified:||20 Apr 2015 13:48|
|Social bookmarking:||Export: EndNote, Zotero | BibTex|
|Look up in GoogleScholar | Find in a UK Library|