Discontinuous Galerkin methods for problems with Dirac delta source

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Houston, Paul and Wihler, Thomas P. (2011) Discontinuous Galerkin methods for problems with Dirac delta source. ESAIM: Mathematical Modelling and Numerical Analysis . ISSN 0764-583X (Submitted)

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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.

Item Type: Article
RIS ID: https://nottingham-repository.worktribe.com/output/1010773
Additional Information: Copyright EDP Sciences.
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Depositing User: Houston, Paul
Date Deposited: 12 Aug 2011 17:09
Last Modified: 04 May 2020 20:23
URI: https://eprints.nottingham.ac.uk/id/eprint/1499

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