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 epsilon-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 epsilon-weighted H(1)-norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Crown Copyright (C) 2010 Published by Elsevier B.V. All rights reserved.