A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points
Numerical Analysis
2020-03-04 v1 Numerical Analysis
Abstract
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with multiple interfaces or with triple-junction points to accommodate interface jump conditions. For non-homogeneous flux jump, we enrich the local approximating spaces by adding up to three local flux basis functions. Numerical experiments are carried out to show that both the Lagrange interpolations and the partial penalized IFEM solutions converge optimally in L2 and H1 norms.
Cite
@article{arxiv.2003.01601,
title = {A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points},
author = {Yuan Chen and Songming Hou and Xu Zhang},
journal= {arXiv preprint arXiv:2003.01601},
year = {2020}
}