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

Journal Article · Fri Oct 31 00:00:00 EDT 2008 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2008.10.007· OSTI ID:1090873

Ju, Lili ^[1]; Tian, Li; Wang, Desheng

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1. University of South Carolina, Columbia, SC

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 R3, 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.

• Research Organization: University of South Carolina, Columbia, SC
• Sponsoring Organization: USDOE; USDOE SC Office of Biological and Environmental Research (SC-23)
• DOE Contract Number: FG02-07ER64431
• OSTI ID: 1090873
• Report Number(s): DOE/FG/ER64431-7
• Journal Information: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Journal Issue: 5-8 Vol. 198; ISSN 0045-7825
• Publisher: Elsevier
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
A posteriori error estimates
Finite volume approximation
PDEs on surfaces