A Priori and a Posteriori Error Estimates of Conforming Discontinuous Galerkin Method for Elliptic Problems

Abstract

The Conforming Discontinuous Galerkin (CDG) method is an innovative numerical approach for solving partial differential equations. Based on the Weak Galerkin (WG) method, it simplifies the numerical scheme by eliminating the stabilizer, substituting the standard WG boundary function with the interior function’s average. In this paper, we propose and analyze a CDG method for second order elliptic problems with variable coefficients. First, optimal a priori error estimates in both the energy norm and the L² norm are established. Then, a residual-type a posteriori error estimator is developed. Furthermore, we prove the efficiency of the a posteriori error estimator. Numerical experiments are conducted to validate the performance of the a priori and a posteriori error estimates.