A posteriori error estimators for discontinuous Galerkin method for diffusion problems, based on the hypercircle method

Abstract In this work, we apply the hypercircle method to Discontinuous Galerkin (DG) approximations of second order diffusion problems featuring inhomogeneous Dirichlet and Neumann boundary conditions. We focus on interior penalty discontinuous (IPDG) in primal variational formulation produce a Prager–Synge theorem for such DG methods. Using method, derive an posteriori error estimator terms equilibrated flux. The is proven be reliable efficient. Numerical results are presented which illustrate estimator’s performance.