A posteriori error estimate for finite volume approximations to singularly perturbed nonlinear convection-diffusion equations

摘要

This paper is devoted to the study of a posteriori and a priori error estimates for the scalar nonlinear convection diffusion equation $c_t + nabla cdot ( u f(c)) - varepsilon Delta c = 0$ . The estimates for the error between the exact solution and an upwind finite volume approximation to the solution are derived in the $L^1$ -norm in the situation, where the diffusion parameter $varepsilon$ is smaller or comparable to the mesh size. Numerical experiments underline the theoretical results.