Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems (Q984913)

The numerical approximation by a lower order anisotropic nonconfirming finite element on appropriately graded meshes is considered for solving singularly perturbed two-dimensional self-adjoint elliptic boundary-value problems. Quasi-optimal order error estimates are proved in the \(\varepsilon\)-weighted \(H^{1}\)-norm valid uniformly, up to a logarithmic factor, in the diffusion parameter. By using the interpolated postprocessing technique, global superconvergent error estimates in \(\varepsilon\)-weighted \(H^{1}\)-norm are obtained. Numerical experiments are carried out to demonstrate validity of the theoretical estimates.