A numerical method for solving three-dimensional elliptic interface problems with triple junction points
A numerical method for solving three-dimensional elliptic interface problems with triple junction points
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DOI：
10.1007/s10444-017-9539-7
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发表时间：
2018-02
影响因子：
1.7
通讯作者：
Liqun Wang;Songming Hou;Liwei Shi
中科院分区：
文献类型：
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作者：
Liqun Wang;Songming Hou;Liwei Shi
多域椭圆接口问题在工程和科学领域有着广泛的应用。然而，由于局部几何复杂性，大多数现有方法在解决多域三维椭圆界面问题时具有挑战性，特别是对于矩阵系数和锐边界面问题。最近有一些针对多域的二维和针对两个域的三维的一些工作。然而，扩展到三维多域椭圆界面问题并非易事。在本文中，我们提出了一种有效的非传统有限元方法，具有非体拟合网格，用于解决多域三维椭圆界面问题。数值实验表明，该方法在分段光滑解的L∞范数上达到了接近二阶的精度。
Elliptic interface problems with multi-domains have wide applications in engineering and science. However, it is challenging for most existing methods to solve three-dimensional elliptic interface problems with multi-domains due to local geometric complexity, especially for problems with matrix coefficient and sharp-edged interface. There are some recent work in two dimensions for multi-domains and in three dimensions for two domains. However, the extension to three dimensional multi-domain elliptic interface problems is non-trivial. In this paper, we present an efficient non-traditional finite element method with non-body-fitting grids for three-dimensional elliptic interface problems with multi-domains. Numerical experiments show that this method achieves close to second order accurate in theL∞norm for piecewise smooth solutions.