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Convergence of numerical solutions to the Allen-Cahn equation. (English) Zbl 0992.65096
From the summary: It is known that the zero level set of the solution of the Allen-Cahn equation $$u_t-\Delta u=\varepsilon^{-2}(u-u^3)$$ approaches, as $$\varepsilon\to 0$$, the solution of the motion by mean curvature flow. In this paper, we consider the convergence of numerical solutions of a discretized Allen-Cahn equation.

##### MSC:
 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs