Superconvergence of Discontinuous Galerkin Method to Nonlinear Differential equations

DOI: 10.5176/2251-1911_CMCGS14.24

Authors: Helmi Temimi

Abstract: In this paper, we investigate the superconvergence
criteria of the discontinuous Galerkin (DG) method applied
to one dimensional nonlinear differential equations. We show
that the p-degree finite element (DG) solution is O(Δx^{p+2})
superconvergent at the roots of specific combined Jacobi polynomials.
Moreover, we used these results to construct efficient and
asymptotically exact a posteriori error estimates.

Keywords: Discontinuous Galerkin method Nonlinear boundary value problem Superconvergence