a1 School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK. Paul.Houston@nottingham.ac.uk
a2 Mathematics Institute, University of Bern, 3012 Bern, Switzerland; email@example.com
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 L2-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.
(Received June 17 2011)
(Revised November 22 2011)
(Online publication May 31 2012)
Mathematics Subject Classification:
∗ Thomas Wihler acknowledges the financial support of the Swiss National Science Foundation (SNF) under Grant No. 200021_126594.