Discontinuous Galerkin methods for problems with Dirac delta source

Houston, Paul; Wihler, Thomas P.

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
• Peer Reviewed: Not Peer Reviewed
• Public URL: https://nottingham-repository.worktribe.com/output/1010773
• Additional Information: Copyright EDP Sciences.