AN ADAPTIVE IMMERSED FINITE ELEMENT METHOD WITH ARBITRARY LAGRANGIAN-EULERIAN SCHEME FOR PARABOLIC EQUATIONS IN TIME VARIABLE DOMAINS

被引：0

作者：

Chen, Zhiming ^{[1
]}

Wu, Zedong ^{[2
]}

Xiao, Yuanming ^{[3
]}

机构：

[1] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, LSEC, Beijing 100190, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math, Beijing 100190, Peoples R China

[3] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

来源：

INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING | 2015年 / 12卷 / 03期

关键词：

Immersed finite element; adaptive; a posteriori error estimate; time variable domain; ALGORITHM;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We first propose an adaptive immersed finite element method based on the a posteriori error estimate for solving elliptic equations with non-homogeneous boundary conditions in general Lipschitz domains. The underlying finite element mesh need not fit the boundary of the domain. Optimal a priori error estimate of the proposed immersed finite element method is proved. The immersed finite element method is then used to solve parabolic problems in time variable domains together with an arbitrary Lagrangian-Eulerian (ALE) time discretization scheme. An a posteriori error estimate for the fully discrete immersed finite element method is derived which can be used to adaptively update the time step sizes and finite element meshes at each time step. Numerical experiments are reported to support the theoretical results.

引用

页码：567 / 591

页数：25