Families of interior penalty hybridizable discontinuous Galerkin methods for second order elliptic problems

Abstract The focus of this paper is the analysis of families of hybridizable interior penalty discontinuous Galerkin methods for second order elliptic problems. We derive a priori error estimates in the energy norm that are optimal with respect to the mesh size. Suboptimal L 2 -norm error estimates are proven. These results are valid in two and three dimensions. Numerical results support our theoretical findings, and we illustrate the computational cost of the method.