An adaptive discontinuous finite volume method for elliptic problems

Authors:
Jiangguo Liu;Lin Mu;Xiu Ye
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
Venue:
Journal of Computational and Applied Mathematics
Year:
2011

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Abstract

An adaptive discontinuous finite volume method is developed and analyzed in this paper. We prove that the adaptive procedure achieves guaranteed error reduction in a mesh-dependent energy norm and has a linear convergence rate. Numerical results are also presented to illustrate the theoretical analysis.