A simple method for matrix-valued coefficient elliptic equations with sharp-edged interfaces

作者：Wang, Liqun; Shi, Liwei^*

来源：Applied Mathematics and Computation, 2014, 242: 917-930.

DOI：10.1016/j.amc.2014.06.084

• Traditional finite element method
• Elliptic equation with matrix-valued coefficients
• Body-fitting grids
• Sharp-edged interface
• Symmetric positive definite

The traditional finite element method has a number of nice properties, and thus it is highly desired for matrix-valued coefficient elliptic equations with sharp-edged interfaces. However, its efficient implementation with body-fitting grids for such problems is highly non-trivial. In this paper, we propose a simple finite element method with body-fitting grids based on semi-Cartesian grid, which makes its implementation fairly straightforward, even for complicated geometry. All possible situations that the interface cuts the grid are considered. Further, the symmetry and positive definiteness of the resulting matrix are ensured for positive definite coefficients. Numerical experiments show that it is second order accurate in the L-infinity norm and numerically very stable.

• 出版日期2014-9-1
• 单位中国石油大学（北京）; 中国政法大学