Open Access

ARTICLE

Distributed Lagrange Multiplier/Fictitious Domain Finite Element Method for a Transient Stokes Interface Problem with Jump Coefficients

Andrew Lundberg¹, Pengtao Sun^1,∗, Cheng Wang², Chen-song Zhang³

1 Department of Mathematical Sciences, University of Nevada, Las Vegas, 4505 Maryland Parkway, Las Vegas, NV 89154, USA.
2 School of Mathematical Sciences, Tongji University, Shanghai, China.
3 LSEC & NCMIS, Academy of Mathematics and System Science, Beijing, China.

* Corresponding Author: Pengtao Sun. Email: .

(This article belongs to the Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)

Computer Modeling in Engineering & Sciences 2019, 119(1), 35-62. https://doi.org/10.32604/cmes.2019.04804

Abstract

The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated.

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Keywords

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