An Interface-Unﬁtted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefﬁcients
Communication in Computational Physics
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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.
Conforming enriched ﬁnite element; Interface-unﬁtted mesh; Stokes-elliptic interface problem; Inf-sup condition; Optimal convergence
An Interface-Unﬁtted Conforming Enriched Finite Element Method for Stokes-Elliptic Interface Problems with Jump Coefﬁcients.
Communication in Computational Physics, 27(4),