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

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

Year:    2020

Author:    Hua Wang, Jinru Chen, Pengtao Sun, Rihui Lan

Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1174–1200

Abstract

In this paper, a conforming enriched finite element method over an interface-unfitted mesh is developed and 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2019-0021

Communications in Computational Physics, Vol. 27 (2020), Iss. 4 : pp. 1174–1200

Published online:    2020-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    27

Keywords:    Conforming enriched finite element interface-unfitted mesh Stokes-elliptic interface problem inf-sup condition optimal convergence.

Author Details

Hua Wang

Jinru Chen

Pengtao Sun

Rihui Lan