Uniform convergence of an upwind finite element method on layer-adapted grids Original Research Article

A singularly perturbed convection–diffusion problem is considered. The problem is discretised using an upwinded finite element method on layer-adapted meshes. We establish convergence of almost first-order in a weighted energy norm, no matter how small the perturbation parameter. As a corollary we derive bounds for the maximum-norm error. Numerical experiments support the theoretical results.