A Posteriori Error Analysis for Systems of Nonlinear Convection-Diffusion Equations

Abstract

In this paper we derive an a posteriori error estimate for the Lagrange-Galerkin discretisation of a nonlinear system of unsteady convection-diffusion problems in two space-dimensions. The proof of the error estimate is based on strong stability estimates of an associated linearised dual problem, together with the Galerkin orthogonality of the finite element method. Based on this a posteriori error estimate, we design the corresponding adaptive algorithm to ensure global control of each component of the discretisation error, with respect to a fixed tolerance.