Error estimates and adaptive finite elements for nonlinear diffusion-convection problems

A priori and a posteriori error estimates are presented for nonlinear diffusion-convection problems when using the classical Streamline Upwind Petrov-Galerkin (SUPG) scheme and numerical integration. For this purpose, an abstract framework is developed. A priori estimates are derived in the H-1 and L(2) norms and the error is bounded above and below by an estimator based on the equation residual. An adaptive algorithm requiring the generation of successive Delaunay triangulations is proposed and numerical results confirm the efficiency of our approach.