A discontinuous hp finite element method for diffusion problems: 1-D analysis

This paper presents the mathematical analysis of a new variant of the discontinuous Galerkin method which is applicable to the numerical solution of diffusion problems, not requiring auxiliary variables such as those used in mixed methods. The focus of this study is on a class of linear second-order boundary value problems for which we prove stability and a priori error estimates in both the finite- and infinite-dimensional spaces.