A hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac delta source

Abstract

In this paper, we investigate a hybridizable discontinuous Galerkin method for second order elliptic equations with Dirac measures. Under assumption that the domain is convex and the mesh is quasi-uniform, a priori error estimate for the error in L2-norm is proved. By duality argument and Oswald interpolation, a posteriori error estimates for the errors in L2-norm and W1,p-seminorm are also obtained. Finally, numerical examples are provided to validate the theoretical analysis.