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

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 R3R3, 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.