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arXiv · 2403.08898

Robust a posteriori error control for the Allen-Cahn equation with variable mobility

Aaron Brunk·Jan Giesselmann·Maria Lukacova-Medvidova
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Abstract

In this work, we derive a $\gamma$-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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Aaron Brunk, Jan Giesselmann, Maria Lukacova-Medvidova. 2024-03-13. Robust a posteriori error control for the Allen-Cahn equation with variable mobility. https://arxiv.org/abs/2403.08898

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