Discontinuous Galerkin methods for problems with Dirac delta source

Houston, Paul; Wihler, Thomas P.

Authors

PAUL HOUSTON paul.houston@nottingham.ac.uk
Professor of Computational and Applied Maths

Thomas P. Wihler

Abstract

In this article we study discontinuous Galerkin finite element discretizations of linear second-order elliptic partial differential equations with Dirac delta right-hand side. In particular, assuming that the underlying computational mesh is quasi-uniform, we derive an a priori bound on the error measured in terms of the L^2-norm. Additionally, we develop residual-based a posteriori error estimators that can be used within an adaptive mesh refinement framework. Numerical examples for the symmetric interior penalty scheme are presented which confirm the theoretical results.

Citation

Houston, P., & Wihler, T. P. Discontinuous Galerkin methods for problems with Dirac delta source. Manuscript submitted for publication

Journal Article Type	Article
Deposit Date	Aug 12, 2011
Journal	ESAIM: Mathematical Modelling and Numerical Analysis
Print ISSN	0764-583X
Electronic ISSN	0764-583X
Publisher	EDP Open
Peer Reviewed	Not Peer Reviewed
Public URL	https://nottingham-repository.worktribe.com/output/1010773
Publisher URL	http://www.esaim-m2an.org/action/displayJournal?jid=MZA
Additional Information	Copyright EDP Sciences.