论文标题
椭圆表PDE的实用相场方法
A Practical Phase Field Method for an Elliptic Surface PDE
论文作者
论文摘要
我们考虑了在给定的封闭的超曲面上求解椭圆PDE的漫射界面方法。该方法基于使用数值正交的（批量）有限元方案，用于相位场函数，因此与其他方法相比，非常容易实现。我们根据空间网格大小，界面宽度和基础正交规则的顺序估算自然规范的误差。给出了数值测试计算，以确认误差边界的形式。
We consider a diffuse interface approach for solving an elliptic PDE on a given closed hypersurface. The method is based on a (bulk) finite element scheme employing numerical quadrature for the phase field function and hence is very easy to implement compared to other approaches. We estimate the error in natural norms in terms of the spatial grid size, the interface width and the order of the underlying quadrature rule. Numerical test calculations are presented which confirm the form of the error bounds.
