Phase field modeling with IGA and FEM : Error surveillance in the transition zone

Markus Klassen, Ingo Münch, Sven Klinkel
The present contribution compares the solution of a phase field problem by the finite element method (FEM) with isogeometric analysis (IGA). For the sake of simplicity, the coupling to additional fields is neglected. Thus, the phase field variable appears as the only unknown in the boundary value problem. The numerical solutions are compared to the analytical solution, elaborated by Falk, of the Allen-Cahn equation. In this model, the Ginzburg-Landau free energy density combines a free Landau
more » ... ergy of sixth order with a quadratic gradient energy. The benchmark consists of a simple quadrilateral geometry with boundary conditions for the phase field variable which allows to solve static unidirectional phase transitions. For the FEM, the mesh is refined uniformly in space by h-and p-refinement. In IGA, the refinement is realized by the knot insertion and order elevation algorithms from computer aided design (CAD) which is known as k-refinement. Furthermore, IGA allows for a higher continuity between the elements which enhances the gradient of the phase transition variable.
doi:10.18154/rwth-2019-03127 fatcat:nxe76uu37nb3tlpv3mjxmr6pfu