Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems

Aayushman Raina, Srinivasan Natesan and Şuayip Toprakseven

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 229, issue C, 203-221

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 H2− norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.

Keywords: Weak Galerkin finite element method; Biharmonic problem; Singular perturbation problem; Shishkin mesh; Anisotropic estimates (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:229:y:2025:i:c:p:203-221

DOI: 10.1016/j.matcom.2024.09.017

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