an:05295224
Zbl 1143.65076
Baňas, L'ubomír; Nürnberg, Robert
Adaptive finite element methods for Cahn-Hilliard equations
EN
J. Comput. Appl. Math. 218, No. 1, 2-11 (2008).
0377-0427
2008
j
65M60 65M06 35M10 35Q53 65M15 65M50
obstacle free energy; finite elements; a posteriori error estimates
Summary: We develop a method for adaptive mesh refinement for steady state problems that arise in the numerical solution of Cahn-Hilliard equations with an obstacle free energy. The problem is discretized in time by the backward-Euler method and in space by linear finite elements. The adaptive mesh refinement is performed using residual based a posteriori estimates; the time step is adapted using a heuristic criterion. We describe the space-time adaptive algorithm and present numerical experiments in two and three space dimensions that demonstrate the usefulness of our approach.