@Article{IJNAM-16-2,
author = {Wang, Cheng and Sun, Pengtao and Zhilin, Li},
title = {​An Iterative Approach for Constructing Immersed Finite Element Spaces and Applications to Interface Problems},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2019},
volume = {16},
number = {2},
pages = {167--191},
abstract = {<p style="text-align: justify;">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 $H^1$, $L^2$<sup>&nbsp;</sup>and $L$<sup>∞</sup> norms, and at least 1.5-th order convergence for the pressure variable in $L^2$&nbsp;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.</p>},
issn = {2617-8710},
doi = {https://doi.org/2019-IJNAM-12798},
url = {https://global-sci.com/article/83057/an-iterative-approach-for-constructing-immersed-finite-element-spaces-and-applications-to-interface-problems}
}