The Immersed Weak Galerkin and Continuous Galerkin Finite Element Method for Elliptic Interface Problem
<|reference_start|>The Immersed Weak Galerkin and Continuous Galerkin Finite Element Method for Elliptic Interface Problem: In this paper, we use the weak Galerkin finite element method to solve the elliptic interface problem on interface-independent meshes. In the interface element, we use the immersed finite element (IFE) functions satisfying the interface conditions precisely and they have optimal approximation capabilities. In the non-interface element, the continuous element is employed to approximate the exact solution. The optimal convergence orders of error are obtained in the $H^1$ norm and $L^2$ norm. A series of numerical experiments are provided to validate the efficiency of the proposed method.<|reference_end|>
@article{yang2024the,
    title={The Immersed Weak Galerkin and Continuous Galerkin Finite Element Method
  for Elliptic Interface Problem},
    author={Lin Yang and Qilong Zhai},
    journal={arXiv preprint arXiv:2409.08480},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.08480},
    primaryClass={math.NA cs.NA}
}