An adaptive refinement method for convection‐diffusion problems

An adaptive finite difference method for singularly perturbed convection‐diffusion problems is presented. The method is introduced using a first‐order upwind scheme and a suitable error estimator based on the first derivatives. To obtain the grid structure needed for the cross stencil a special refinement strategy is considered. To avoid the slave points we change the stencil at the interface points from a cross to a skew one. After the convergence of the refinement algorithm we use a combination of a first order upwind and a second order central schemes to achieve higher order of convergence. Several numerical examples show the efficiency of our treatment. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)