Achieving Superconvergence by One-Dimensional Discontinuous Finite Elements: The CDG Method

Abstract

. Novelty of this work is the development of a finite element method using discontinuous P k element, which has two-order higher convergence rate than the optimal order. The method is used to solve a one-dimensional second order elliptic problem. A totally new approach is developed for error analysis. Superconvergence of order two for the CDG finite element solution is obtained. The P k solution is lifted to an optimal order P k + 2 solution elementwise. The numerical results confirm the theory.