Speaker：Zhiming Chen (Chinese Academy of Sciences)

Time：2024-11-18, 16:30

Location：Conference Room C503 at Administration Building at Haiyun Campus

Abstract:

We consider high-order unfitted finite element methods on Cartesian meshes with hanging nodes for elliptic interface problems, which release the work of body-fitted mesh generation and allow us to design adaptive finite element methods for solving curved geometric singularities. We introduce new concepts of the large element and interface deviation to solve the small cut cell problem of unfitted finite element methods. We consider the reliable implementation of the adaptive method, which extends 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. This talk is based on joint works with Ke Li, Yong Liu and Xueshuang Xiang.