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Research

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Publication details for Dr Stefano Giani

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): 1250030.

Author(s) from Durham

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.