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• W2964804939 abstract "This work is concerned with the proof of emph{a posteriori} error estimates for fully-discrete Galerkin approximations of the Allen-Cahn equation in two and three spatial dimensions. The numerical method comprises of the backward Euler method combined with conforming finite elements in space. For this method, we prove conditional type emph{a posteriori} error estimates in the $L^{}_4(0,T;L^{}_4(Omega))$-norm that depend polynomially upon the inverse of the interface length $epsilon$. The derivation relies crucially on the availability of a spectral estimate for the linearized Allen-Cahn operator about the approximating solution in conjunction with a continuation argument and a variant of the elliptic reconstruction. The new analysis also appears to improve variants of known emph{a posteriori} error bounds in $L_2(H^1)$, $L_infty^{}(L_2^{})$-norms in certain regimes." @default.
• W2964804939 created "2019-08-13" @default.
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• W2964804939 date "2019-07-29" @default.
• W2964804939 modified "2023-09-26" @default.
• W2964804939 title "A posteriori error estimates for the Allen-Cahn problem" @default.
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