Schur's Complement and Discontinuous Galerkin Methods for Domain Decomposition Solvers and Plasticity and Interface Evolution Analyses

Abstract

Adaptive methods can be based on either conforming or non-conforming meshes. Though non-conforming meshes are easier to generate, they require the satisfaction of jump conditions across the non-conforming interface. In this work we develop a discontinuous Galerkin framework for such an adaptive mesh refinement. An advantage of discontinuous Galerkin schemes is that they do not introduce constraint equations and their resulting Lagrange multiplier fields as done in mixed and mortar methods. Without loss of generality we demonstrate our method by analyzing the Stefan problem of solidification.