Optimal and Robust A Posteriori Error Estimates in L
نویسندگان
چکیده
Optimal a posteriori error estimates in L∞(0, T ; L(Ω)) 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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