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


Raina A., Natesan S., TOPRAKSEVEN Ş.

Mathematics and Computers in Simulation, vol.229, pp.203-221, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 229
  • Publication Date: 2025
  • Doi Number: 10.1016/j.matcom.2024.09.017
  • Journal Name: Mathematics and Computers in Simulation
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Page Numbers: pp.203-221
  • Keywords: Anisotropic estimates, Biharmonic problem, Shishkin mesh, Singular perturbation problem, Weak Galerkin finite element method
  • Yozgat Bozok University Affiliated: Yes

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.