Error measurement and FEM benchmark for phase field modeling

Solid-state phase-transformation often deals with coupled field variables like mechanical stress or electric potential on different scales compared to the size of phase transition. Further, highly nonlinear equations rule the phase parameter. Thus, required mesh density to approximate phase field variables is often higher than for coupled fields. Finite element techniques applying h- or p-adaptivity can help to increase the efficiency of such simulations. Therefore, it is important to define a benchmark test to verify numerical approaches. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)