Robust a posteriori error control for the Allen-Cahn equation with variable mobility
CoRR(2024)
Abstract
In this work, we derive a γ-robust a posteriori error estimator for
finite element approximations of the Allen-Cahn equation with variable
non-degenerate mobility. The estimator utilizes spectral estimates for the
linearized steady part of the differential operator as well as a conditional
stability estimate based on a weighted sum of Bregman distances, based on the
energy and a functional related to the mobility. A suitable reconstruction of
the numerical solution in the stability estimate leads to a fully computable
estimator.
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