Devising superconvergent HDG methods by M-decompositions

Abstract

In this thesis, we develop the concept of an M-decomposition as an effective tool for devising high-order accurate hybridizable discontinuous Galerkin methods and hybridized mixed methods that superconverge on unstructured meshes of shape-regular polyhedral elements for three linear elliptic partial differential equations, namely, the (steady-state) diffusion equation, the equations for linear elasticity, and the equations for incompressible Stokes flow.