A weak Galerkin finite element method for solving the asymptotic lower bound of Maxwell eigenvalue problem
<|reference_start|>A weak Galerkin finite element method for solving the asymptotic lower bound of Maxwell eigenvalue problem: In this paper, we propose a weak Galerkin (WG) finite element method for the Maxwell eigenvalue problem. By restricting subspaces, we transform the mixed form of Maxwell eigenvalue problem into simple elliptic equation. Then we give the WG numerical scheme for the Maxwell eigenvalue problem. Furthermore, we obtain the optimal error estimates of arbitrarily high convergence order and prove the lower bound property of numerical solutions for eigenvalues. Numerical experiments show the accuracy of theoretical analysis and the property of lower bound.<|reference_end|>
@article{li2024a,
    title={A weak Galerkin finite element method for solving the asymptotic lower
  bound of Maxwell eigenvalue problem},
    author={Shusheng Li and Qilong Zhai},
    journal={arXiv preprint arXiv:2405.13423},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.13423},
    primaryClass={math.NA cs.NA}
}