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

Abstract

SUMMARYThe numerical approximation by a lower-order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular 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.