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.

中文翻译：

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椭圆表面偏微分方程的实用相场法

我们考虑在给定的封闭超曲面上求解椭圆偏微分方程的漫反射界面方法。该方法基于对相场函数采用数值求积的（体）有限元方案，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阶数估计自然范数的误差。给出了数值测试计算，确认了误差范围的形式。