Journal
MATHEMATICS OF COMPUTATION
Volume 80, Issue 274, Pages 761-780Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0025-5718-2010-02444-5
Keywords
Allen-Cahn equation; mean curvature flow; finite element method; error analysis; adaptive methods
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Quasi-optimal a posteriori error estimates in L-infinity(0, T; L-2(Omega)) are derived for the finite element approximation of Allen-Cahn equations. The estimates depend on the inverse of a small parameter only in a low order polynomial and are valid past topological changes of the evolving interface. The error analysis employs an elliptic reconstruction of the approximate solution and applies to a large class of conforming, nonconforming, mixed, and discontinuous Galerkin methods. Numerical experiments illustrate the theoretical results.
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