An Iterative Approach for Constructing Immersed Finite Element Spaces and Applications to Interface Problems
Year: 2019
Author: Cheng Wang, Pengtao Sun, Zhilin Li
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 167–191
Abstract
In this paper, an iterative approach for constructing immersed finite element spaces is developed for various interface conditions of interface problems involving multiple primary variables. Combining such iteratively constructed immersed finite element spaces with the distributed Lagrange multiplier/fictitious domain (DLM/FD) method, we further present a new discretization method that can uniformly solve general interface problems with multiple primary variables and/or with different governing equations on either side of the interface, including fluid-structure interaction problems. The strengths of the proposed method are shown in the numerical experiments for Stokes- and Stokes/elliptic interface problems with different types of interface conditions, where, the optimal or nearly optimal convergence rates are obtained for the velocity variable in $H^1$, $L^2$ and $L$∞ norms, and at least 1.5-th order convergence for the pressure variable in $L^2$ norm within few number of iterations. In addition, numerical experiments show that such iterative process uniformly converges and the number of iteration is independent of mesh ratios and jump ratios.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2019-IJNAM-12798
International Journal of Numerical Analysis and Modeling, Vol. 16 (2019), Iss. 2 : pp. 167–191
Published online: 2019-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25
Keywords: Immersed finite element (IFE) method fictitious domain method Lagrange multiplier iterative process interface problems fluid-structure interactions (FSI).