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A posteriori error estimates for finite volume approximations of elliptic equations on general surfaces

✍ Scribed by Lili Ju; Li Tian; Desheng Wang

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 678 KB
Volume: 198
Category: Article
ISSN: 0045-7825
DOI: 10.1016/j.cma.2008.10.007

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✦ Synopsis

In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady convection-diffusion-reaction equations defined on surfaces in R 3 , which are often implicitly represented as level sets of smooth functions. Reliability and efficiency of the proposed a posteriori error estimator are rigorously proved. Numerical experiments are also conducted to verify the theoretical results and demonstrate the robustness of the error estimator.

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