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

Abstract 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.