In this paper,we first review the recent progress of unfitted finite element methods for solving elliptic equations on domains with complex geometry.Then we propose an arbitrarily high-order conforming unfitted finite element method defined on automatically generated induced meshes from Cartesian meshes with hanging nodes.The induced mesh allows us to use a simple treatment of the hp finite element method to deal with the hanging nodes to construct a high-order conforming finite element space.Nitsche techniques are used to deal with the Dirichlet boundary conditions.The stability and the hp a priori error estimates of our methods are established.Numerical examples confirm our theoretical findings.
关键词
非拟合网格有限元/hp先验误差估计/网格自动生成
Key words
unfitted finite element/hp a priori error estimate/automatic mesh generation
维普
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