Convergence of the discontinuous finite volume method for elliptic problems with minimal regularity

Authors:
Jiangguo Liu;Lin Mu;Xiu Ye;Rabeea Jari
Affiliations:
Department of Mathematics, Colorado State University, Fort Collins, CO 80523-1874, USA;Department of Applied Science, University of Arkansas at Little Rock, Little Rock, AR 72204, USA;Department of Mathematics, University of Arkansas at Little Rock, Little Rock, AR 72204, USA;Department of Applied Science, University of Arkansas at Little Rock, Little Rock, AR 72204, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2012

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Abstract

This paper investigates convergence of the discontinuous finite volume method (DFVM) under minimal regularity assumptions on solutions of second order elliptic boundary value problems. Conventional analysis requires the solutions to be in Sobolev spaces H^1^+^s,s12. Here we assume the solutions are in H^1^+^s,s0 and employ the techniques developed in Gudi (2010) [18,20] to derive error estimates in a mesh-dependent energy norm and the L"2-norm for DFVM. The theoretical estimates are illustrated by numerical results, which include problems with corner singularity and intersecting interfaces.