An h-narrow band finite-element method for elliptic equations on implicit surfaces
An h-narrow band finite-element method for elliptic equations on implicit surfaces
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DOI：
10.1093/imanum/drn049
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发表时间：
2010-04-01
影响因子：
2.1
通讯作者：
Heine, Claus-Justus
中科院分区：
文献类型：
--
作者：
Deckelnick, Klaus;Dziuk, Gerhard;Heine, Claus-Justus
本文定义了求解由水平集函数隐式给出的曲线或曲面上的椭圆型偏微分方程的有限元方法。该方法是专门为复杂曲面设计的。关键思想是在表面周围的窄带上解决偏微分方程。带的宽度与网格大小成正比。我们使用不适合窄带的有限元空间，这样元素就被切断了。然而，实现起来很容易。我们证明了曲面上泊松方程最优阶的误差估计，并给出了数值测试和实例。
In this article we define a finite-element method for elliptic partial differential equations (PDEs) on curves or surfaces, which are given implicitly by some level set function. The method is specially designed for complicated surfaces. The key idea is to solve the PDE on a narrow band around the surface. The width of the band is proportional to the grid size. We use finite-element spaces that are unfitted to the narrow band, so that elements are cut off. The implementation nevertheless is easy. We prove error estimates of optimal order for a Poisson equation on a surface and provide numerical tests and examples.