Discontinuous Galerkin Methods for Semilinear Elliptic Boundary Value Problem

Abstract

A discontinuous Galerkin (DG) scheme for solving semilinear elliptic problem is developed and analyzed in this paper. The DG finite element discretization is first established, then the corresponding well-posedness is provided by using Brouwer’s fixed point method. Some optimal priori error estimates under both DG norm and $L^2$ norm are presented, respectively. Numerical results are given to illustrate the efficiency of the proposed approach.