Efficient and reliable finite element techniques for phase field models
M. Stiemer, A. Groß-Wöhrmann, S. Gladkov, B. Svendsen, R. Spatschek, I. Steinbach.
International Journal of Materials Research, 101, 498-502, (2010)
In this work auto-adaptive finite-element techniques are presented that allow for quantitatively reliable numerical computation of phase field models. These techniques are based on goal oriented error estimation for finite elements with dual weighted residuals and algorithms for auto-adaptive mesh adaptation in space and in time. It is discussed for which kind of problems the computational overhead of such methods is expected to be justified by a sufficient reduction of the problem size.