Micromagnetics is a continuum variational theory describing magnetization patterns in
ferromagnetic media. Its multiscale nature due to different inherent spatiotemporal physical …

Our work on rate-independent systems was stimulated by our search for evolutionary
material models for shape-memory alloys that are flexible enough to encompass nonlinear …

In variational phase-field modeling of brittle fracture, the functional to be minimized is not
convex, so that the necessary stationarity conditions of the functional may admit multiple …

In this work, we study numerical issues related to a common mathematical model which
describes ferromagnetic materials, both in a stationary and nonstationary context …

The variational model by Landau and Lifshitz is frequently used in the simulation of
stationary micromagnetic phenomena. We consider the limit case of large and soft magnetic …

We present a numerical method for the approximation of microstructure in martensitic
crystals by piecewise laminates, and we give computational results for several three …

We study the approximation properties of piecewise constant functions with respect to
triangular and rectangular finite elements in a metric defined on functions of bounded …

The proposed model combines tendency for minimization of Gibbs' magnetic energy with the
rate-independent maximum-dissipation mechanism that reflects the macroscopic quantity of …

We propose a new approach to the numerical treatment of non (quasi) convex rate-
independent evolutionary problems. The main idea is to replace the original microscopic …

This paper addresses the numerical approximation of Young measures appearing as
generalized solutions to scalar nonconvex variational problems. We prove a priori and a …