Superconvergence byM-decompositions. Part II: Construction of two-dimensional finite elements

Abstract

We apply the concept of an M -decomposition introduced in Part I to systematically construct local spaces defining superconvergent hybridizable discontinuous Galerkin methods, and their companion sandwiching mixed methods. This is done in the framework of steady-state diffusion problems for the h - and p -versions of the methods for general polygonal meshes in two-space dimensions.