Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms

Toprakseven Ş., Zhu P.

Applied Mathematics and Computation, cilt.441, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 441
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1016/j.amc.2022.127683
  • Dergi Adı: Applied Mathematics and Computation
  • 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, Civil Engineering Abstracts
  • Anahtar Kelimeler: Balanced norm, Shishkin mesh, Singularly perturbed boundary value problems, Two-parameter differential equations, Uniform convergence, Weak galerkin finite element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

A weak Galerkin finite element method is proposed for solving singularly perturbed problems with two parameters. A robust uniform optimal convergence has been proved in the corresponding energy and a stronger balanced norms using piecewise higher order discontinuous polynomials on a piecewise uniform Shishkin mesh. Finally, we give some numerical experiments to support theoretical results.