A‐posteriori error analysis and adaptive finite element methods for singularly perturbed convection‐diffusion equations

Abstract

Abstract For singularly perturbed one‐dimensional convection‐diffusion equations, finite element approximations are constructed based on a so‐called approximate symmetrization of the given unsymmetric problem. Local a‐posteriori error estimates are established with respect to an appropriate energy norm where the bounds are proved to be realistic. The local bounds, called error indicators, provide a basis for a self‐adaptive mesh refinement. For a model problem numerical results are presented showing that the adaptive method detects and resolves the boundary layer.