A Discontinuous Finite Element Method for Solving a Multiwell Problem

Abstract. Many physical materials of practical relevance can attain several variants of crystalline microstructure. The appropriate energy functional is necessarily non-convex, and the minimization of the functional becomes a challenging problem. A new numerical method based on discontinuous nite elements and a scaled energy functional is proposed. It exhibits excellent convergence behavior for the energy (second order) as well as other crucial quantities of interest for general spatial meshes, contrary to standard (non-) conforming methods. Both theoretical analyses and numerical test calculations are presented and contrasted to other current nite element methods for this problem.