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

A 2008 Preprint by L. Ju, L. Tian, and D. Wang

• 2008:03

• In this paper, we present a residual-based a posteriori error estimate for the finite volume discretization of steady diffusion-convection-reaction equations defined on general 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.