Higher-degree rectangular immersed finite elements discontinuous Galerkin methods for elliptic interface problems

doi:10.1016/j.cam.2025.117126

Higher-degree rectangular immersed finite elements discontinuous Galerkin methods for elliptic interface problems

2025-10-01

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DOI：10.1016/j.cam.2025.117126

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We propose and analyze higher-degree rectangular immersed finite elements (IFE) for elliptic interface problems. These IFE functions are constructed by a Cauchy extension. Properties of the proposed IFE functions are analyzed, including the optimal approximation capability of the resulting IFE spaces, as well as inverse and trace inequalities. The higher-degree rectangular IFE spaces are employed in discontinuous Galerkin (DG) formulations to solve the elliptic interface problems. The optimal error estimates for the proposed DGIFE methods in both an energy and L2 norms are derived. Numerical results are provided to illustrate the convergence of the proposed DGIFE methods.

Keywords:

Immersed finite element methods

Higher degree rectangular elements

Discontinuous Galerkin

Interface problems

Higher-degree rectangular immersed finite elements discontinuous Galerkin methods for elliptic interface problems

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