Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction–diffusion problems

The numerical approximation by a lower order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving singular perturbation problems. The quasi-optimal order error estimates are proved in the ε -weighted H 1 -norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in ε -weighted H 1 -norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis.