Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems
<|reference_start|>Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems: We consider the Weak Galerkin finite element approximation of the Singularly Perturbed Biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent $H^{2}-$ norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.<|reference_end|>
@article{raina2024anisotropic,
    title={Anisotropic Error Analysis of Weak Galerkin finite element method for
  Singularly Perturbed Biharmonic Problems},
    author={Aayushman Raina, Srinivasan Natesan and c{S}uayip Toprakseven},
    journal={arXiv preprint arXiv:2409.07217},
    year={2024},
    archivePrefix={arXiv},
    eprint={2409.07217},
    primaryClass={math.NA cs.NA}
}