A weak Galerkin finite element method for singularly perturbed problems with two small parameters on Bakhvalov-type meshes

Toprakseven Ş., Kaushik A., Sharma M.

Numerical Algorithms, cilt.97, sa.2, ss.727-751, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 97 Sayı: 2
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s11075-023-01721-8
  • Dergi Adı: Numerical Algorithms
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.727-751
  • Anahtar Kelimeler: 34K26, 65N30, 65N50, Bakhvalov-type mesh, Balanced norm, Optimal order convergence, Two-parameter singularly perturbed differential equation, Weak Galerkin finite element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

A weak Galerkin finite element method is proposed and analyzed for solving two-parameter singularly perturbed differential equations on Bakhvalov-type meshes. A robust optimal order convergence has been presented in the related energy and the balanced norms based on carefully defined penalization terms using piecewise higher order discontinuous functions in the interior of the mesh and single-valued zero order polynomial on the skeleton of the mesh. A special interpolation operator which deals with the difficulty arising from the standard interpolation error estimates on the Bakhvalov-type meshes is constructed. Finally, we give some numerical experiments to support theoretical results.