An Interface-Unfitted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefficients

Document Type

Article

Publication Date

2-1-2020

Publication Title

Communication in Computational Physics

Volume

27

Issue

4

First page number:

1174

Last page number:

1200

Abstract

In this paper, a conforming enriched finite element method over an interfaceunfitted mesh is developedand analyzed for a type of Stokes-elliptic interface problem with jump coefficients. An inf-sup stability result that is uniform with respect to the mesh size is proved in order to derive the corresponding well-posedness and optimal convergence properties in spite of the low regularity of the problem. The developed new finite element method breaks the limit of the classical immersed finite element method (IFEM) which can only deal with the case of identical governing equations on either side of the interface. Numerical experiments are carried out to validate the theoretical results. This is the first step of our new method to solve complex interface problems with different governing equations on either side of the interface, and will be extended to solve transient interface problems towards fluid-structure interaction problems in the future.

Keywords

Conforming enriched finite element; Interface-unfitted mesh; Stokes-elliptic interface problem; Inf-sup condition; Optimal convergence

Disciplines

Mathematics

Language

English

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