A bound-preserving scheme for the Allen-Cahn equation
Résumé
We propose and analyze a bound-preserving scheme for the Allen-Cahn equation. We derive an error estimate that is optimal in the $L^2(H^1)$-seminorm and has only a polynomial dependence on $\epsilon^{-1}$. Numerical experiments are conducted to compare the performance of our scheme with an operator-splitting scheme.
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