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In this article, we introduce a new partially penalized immersed finiteelement method (IFEM) for solving elliptic interface problems withmulti-domains and triple-junction points. We construct new IFE functions onelements intersected with multiple interfaces or with triple-junction points toaccommodate interface jump conditions. For non-homogeneous flux jump, we enrichthe local approximating spaces by adding up to three local flux basisfunctions. Numerical experiments are carried out to show that both the Lagrangeinterpolations and the partial penalized IFEM solutions converge optimally inL2 and H1 norms.

A Bilinear Partially Penalized Immersed Finite Element Method for Elliptic Interface Problems with Multi-Domains and Triple-Junction Points