A posteriori error estimate of the discontinuous Galerkin method with Lagrange multiplier for elliptic problems

Abstract

This study aims to derive and analyze an a posteriori error estimator for the solution of the discontinuous Galerkin method with Lagrange multiplier (DGLM) for the elliptic problems with nonhomogeneous Dirichlet boundary condition $u=g$ for g in $H^{1/2}(\partial \Omega )$. A general version of the DGLM method is derived. Strong stability of the solution of the DGLM method is proved. Edgewise iterative scheme for the general DGLM method is described.