论文标题
用于变形表面的Allen-CAHN方程的有限元方法
A finite element method for Allen-Cahn equation on deforming surface
论文作者
论文摘要
该论文研究了在时间依赖性表面上定义的艾伦-CAHN型方程，该方程是相位分离模型，并在薄材料层中使用订单diSorder跃迁。通过形式的内管扩展，可以表明溶液的限制行为是参考坐标中的测地均值曲率流。对于方程式的数值解，考虑了一种几何有限元法，称为痕量FEM。本文提供了完全稳定性分析和收敛分析，这些分析说明了插值误差和几何形状的近似恢复。
The paper studies an Allen-Cahn-type equation defined on a time-dependent surface as a model of phase separation with order-disorder transition in a thin material layer. By a formal inner-outer expansion, it is shown that the limiting behavior of the solution is a geodesic mean curvature type flow in reference coordinates. A geometrically unfitted finite element method, known as a trace FEM, is considered for the numerical solution of the equation. The paper provides full stability analysis and convergence analysis that accounts for interpolation errors and an approximate recovery of the geometry.
