Error Estimates for the Adaptive Computation of a Scalar Three Well Problem

Abstract

We investigate the numerical approximation of Young measure solutions appearing as generalised solutions in scalar non-convex variational problems. A priori and a posteriori error estimates for a macroscopic quantity, i.e., the stress, are given. Numerical experiments for a scalar three well problem, occurring as a subproblem in the theory of phase transitions in crystalline solids, show that the computational effort can be significantly reduced using an adaptive mesh-refinement strategy combined with an active set technique by Carstensen and Roubíček.