20150327
We consider AllenCahn and CahnHilliard equations as phase field models with constant and variable mobility. Both equations are discretized in space using symmetric interior penalty discontinuous Galerkin (SIPG) finite elements. Time discretization is performed by the energy stable average vector field (AVF) method for gradient systems like AllenCahn equation. We show that the fully discrete scheme satisfies the energy decreasing property. The numerical results for one and two dimensional AllenCahn and CahnHilliard equations using adaptive stepping confirm that the discrete energy decreases monotonically, the phase separation and metastability phenomena can be observed and the ripening time is detected correctly for convex double well and nonconvex logarithmic energy functionals.
Category: CE SeminarTechnische Universität Darmstadt
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