Mathematics > Numerical Analysis
[Submitted on 6 Mar 2024
]
Title: An arbitrarily high order unfitted finite element method for elliptic interface problems with automatic mesh generation, Part II. Piecewise-smooth interfaces
Title: 任意高阶非匹配有限元方法用于椭圆界面问题的自动网格生成，第二部分。 分片光滑界面
Abstract: We consider the reliable implementation of an adaptive high-order unfitted finite element method on Cartesian meshes for solving elliptic interface problems with geometrically curved singularities. We extend our previous work on the reliable cell merging algorithm for smooth interfaces to automatically generate the induced mesh for piecewise smooth interfaces. An $hp$ a posteriori error estimate is derived for a new unfitted finite element method whose finite element functions are conforming in each subdomain. Numerical examples illustrate the competitive performance of the method.
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