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

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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.

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Acknowledgements

The authors were partially supported by NSF Grant DMS-1418806.

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  1. Department of Mathematical Sciences, University of Nevada Las Vegas, 4505 Maryland Parkway, Las Vegas, NV, 89154, USA

    Rihui Lan & Pengtao Sun

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  1. Rihui Lan
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  2. Pengtao Sun
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Correspondence to Pengtao Sun.

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Lan, R., Sun, P. A Monolithic Arbitrary Lagrangian–Eulerian Finite Element Analysis for a Stokes/Parabolic Moving Interface Problem. J Sci Comput 82, 59 (2020). https://doi.org/10.1007/s10915-020-01161-9

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  • DOI: https://doi.org/10.1007/s10915-020-01161-9

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