A Monolithic Arbitrary Lagrangian–Eulerian Finite Element Analysis for a Stokes/Parabolic Moving Interface Problem

Document Type

Article

Publication Date

2-17-2020

Publication Title

Journal of Scientific Computing

Volume

82

First page number:

1

Last page number:

36

Abstract

In this paper, an arbitrary Lagrangian–Eulerian (ALE)—finite element method (FEM) is developed within the monolithic approach for a moving-interface model problem of a transient Stokes/parabolic coupling with jump coefficients—a linearized fluid-structure interaction (FSI) problem. A new H^1-projection is defined for this problem for the first time to account for the mesh motion due to the moving interface. The well-posedness and optimal convergence properties in both the energy norm and L^2 norm are analyzed for this mixed-type H^1-projection, with which the stability and optimal error estimate in the energy norm are derived for both semi- and fully discrete mixed finite element approximations to the Stokes/parabolic interface problem. Numerical experiments are carried out to validate all theoretical results. The developed analytical approach can be extended to a general FSI problem.

Keywords

Stokes/parabolic interface problem; Arbitrary Lagrangian–Eulerian (ALE) mapping; H1-projection; Mixed finite element; Optimal error estimates; Stability analysis

Disciplines

Mathematics

Language

English

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