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, cilt.229, ss.203-221, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 229
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1016/j.matcom.2024.09.017
  • Dergi Adı: Mathematics and Computers in Simulation
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, Public Affairs Index, zbMATH
  • Sayfa Sayıları: ss.203-221
  • Anahtar Kelimeler: Anisotropic estimates, Biharmonic problem, Shishkin mesh, Singular perturbation problem, Weak Galerkin finite element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

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.