Convergence and superconvergence analysis of finite element methods on graded meshes for singularly and semisingularly perturbed reaction-diffusion problems (Q939539)

The authors consider bilinear finite element methods on appropriately graded meshes for solving singular and semisingular perturbation problems. They first prove quasi-optimal order error estimates in an \(\varepsilon\)-weighted \(H^1\)-norm uniformly in the singular perturbation parameter \(\varepsilon\), up to a logarithmic factor. Then they obtain global superconvergent error estimates in the \(\varepsilon\)-weighted \(H^1\)-norm by using the interpolation postprocessing technique. Furthermore, they give numerical experiments to demonstrate the validity of their theoretical analysis.