Superconvergence of the hh-pp version of the finite element method in one dimension

In this paper, we investigate the superconvergence properties of the hh-pp version of the finite element method (FEM) for two-point boundary value problems. A postprocessing technique for the hh-pp finite element approximation is analyzed. The analysis shows that the postprocess improves the order of convergence. Furthermore, we obtain asymptotically exact a posteriori error estimators based on the postprocessing results. Numerical examples are included to illustrate the theoretical analysis.