Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems
Numerical Analysis
2024-09-12 v1 Numerical Analysis
Abstract
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 norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.
Cite
@article{arxiv.2409.07217,
title = {Anisotropic Error Analysis of Weak Galerkin finite element method for Singularly Perturbed Biharmonic Problems},
author = {Aayushman Raina and Srinivasan Natesan and Şuayip Toprakseven},
journal= {arXiv preprint arXiv:2409.07217},
year = {2024}
}