Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D
<|reference_start|>Convergence analysis of a weak Galerkin finite element method on a Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation in 2D: In this paper, we propose a weak Galerkin finite element method (WG) for solving singularly perturbed convection-diffusion problems on a Bakhvalov-type mesh in 2D. Our method is flexible and allows the use of discontinuous approximation functions on the meshe. An error estimate is devised in a suitable norm and the optimal convergence order is obtained. Finally, numerical experiments are given to support the theory and to show the efficiency of the proposed method.<|reference_end|>
@article{liu2024convergence,
    title={Convergence analysis of a weak Galerkin finite element method on a
  Bakhvalov-type mesh for a singularly perturbed convection-diffusion equation
  in 2D},
    author={Shicheng Liu, Xiangyun Meng, and Qilong Zhai},
    journal={arXiv preprint arXiv:2405.15136},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.15136},
    primaryClass={math.NA cs.NA}
}