Volume 11, Issue 5
An Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domain and Triple Junction Points

Yuan Chen ,  Songming Hou and Xu Zhang

10.4208/aamm.OA-2018-0175

Adv. Appl. Math. Mech., 11 (2019), pp. 1005-1021.

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  • Abstract

Interface problems have wide applications in modern scientific research. Obtaining accurate numerical solutions of multi-domain problems involving triple junction conditions remains a significant challenge. In this paper, we develop an efficient finite element method based on non-body-fitting meshes for solving multi-domain elliptic interface problems. We follow the idea of immersed finite element by modifying local basis functions to accommodate interface conditions. We enrich the local finite element space by adding new basis functions for handling non-homogeneous flux jump. The numerical scheme is symmetric and positive definite.  Numerical experiments are provided to demonstrate the features of our method.

  • History

Published online: 2019-06

  • AMS Subject Headings

35R05, 65N15, 65N30

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