Volume 18, Issue 3
The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem

Ian Kesler, Rihui Lan & Pengtao Sun

Int. J. Numer. Anal. Mod., 18 (2021), pp. 339-361.

Published online: 2021-03

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  • 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.

  • Keywords

Arbitrary Lagrangian-Eulerian (ALE) method, mixed finite element method (FEM), fluid-structure interactions (FSI), Stokes/parabolic interface problem, stability, optimal convergence.

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@Article{IJNAM-18-339, author = {Kesler , Ian and Lan , Rihui and Sun , Pengtao}, title = {The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2021}, volume = {18}, number = {3}, pages = {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.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/18719.html} }
TY - JOUR T1 - The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem AU - Kesler , Ian AU - Lan , Rihui AU - Sun , Pengtao JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 339 EP - 361 PY - 2021 DA - 2021/03 SN - 18 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/18719.html KW - Arbitrary Lagrangian-Eulerian (ALE) method, mixed finite element method (FEM), fluid-structure interactions (FSI), Stokes/parabolic interface problem, stability, optimal convergence. AB -

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.

Ian Kesler, Rihui Lan & Pengtao Sun. (2021). The Arbitrary Lagrangian-Eulerian Finite Element Method for a Transient Stokes/Parabolic Interface Problem. International Journal of Numerical Analysis and Modeling. 18 (3). 339-361. doi:
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