An adaptive discontinuous finite volume method for elliptic problems

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 analy...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2011-07, Vol.235 (18), p.5422-5431
Main Authors: Liu, Jiangguo, Mu, Lin, Ye, Xiu
Format: Article
Language:English
Subjects:
a posteriori error estimates
Acceleration of convergence
Adaptive mesh refinements
Computation
Convergence
Direct power generation
Elliptic boundary value problems
Error reduction
Exact sciences and technology
Finite volume method
Finite volume methods
Mathematical analysis
Mathematical models
Mathematics
Norms
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations, boundary value problems
Sciences and techniques of general use
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Summary: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. ► An adaptive discontinuous finite volume method (DFVM) is developed. ► The adaptive DFVM achieves guaranteed error reduction. ► The adaptive DFVM is asymptotically optimal as nonlinear approximation.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2011.05.051