The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem
Year: 2021
Author: Ian Kesler, Rihui Lan, Pengtao Sun
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 339–361
Abstract
In this paper, a type of nonconservative arbitrary Lagrangian-Eulerian (ALE) finite
element method is developed and analyzed in the monolithic frame for a transient Stokes/parabolic
moving interface problem with jump coefficients. The mixed and the standard finite element
approximations are adopted for the transient Stokes equations and the parabolic equation on
either side of the moving interface, respectively. The stability and optimal convergence properties
of both semi- and full discretizations are analyzed in terms of the energy norm. The developed
numerical method can be generally extended to the realistic fluid-structure interaction (FSI)
problems in a time-dependent domain with a moving interface.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2021-IJNAM-18719
International Journal of Numerical Analysis and Modeling, Vol. 18 (2021), Iss. 3 : pp. 339–361
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Arbitrary Lagrangian-Eulerian (ALE) method mixed finite element method (FEM) fluid-structure interactions (FSI) Stokes/parabolic interface problem stability optimal convergence.