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

Summary.

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.