The Mathematical Institute, University of Oxford, Eprints Archive

Variational Convergence of IP-DGFEM

Buffa, Annalisa and Ortner, Christoph (2007) Variational Convergence of IP-DGFEM. Technical Report. Unspecified. (Submitted)

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Abstract

In this paper, we develop the theory required to perform a variational convergence analysis for discontinuous Galerkin nite element methods when applied to minimization problems. For Sobolev indices in $\left[1;\infty\right)$, we prove generalizations of many techniques of classical analysis in Sobolev spaces and apply them to a typical energy minimization problem for which we prove convergence of a variational interior penalty discontinuous Galerkin nite element method (VIPDGFEM). Our main tool in this analysis is a theorem which allows the extraction of a "weakly" converging subsequence of a family of discrete solutions and which shows that any "weak limit" is a Sobolev function.

Item Type:Technical Report (Technical Report)
Subjects:H - N > Numerical analysis
Research Groups:Numerical Analysis Group
ID Code:1092
Deposited By:Lotti Ekert
Deposited On:07 May 2011 09:02
Last Modified:07 May 2011 09:02

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