An efficient operator splitting weak Galerkin method for singularly perturbed 2D parabolic PDEs

Raina A., Natesan S., TOPRAKSEVEN Ş.

Numerical Algorithms, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1007/s11075-025-02152-3
  • Dergi Adı: Numerical Algorithms
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: ADI-type method, Convergence analysis, Operator-splitting method, Piecewise-uniform Shishkin mesh, Singularly perturbed 2D parabolic PDEs, Stability, WG-FEM
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

In this paper, we have introduced an operator splitting weak Galerkin finite element method (WG-FEM) for a class of second order singularly perturbed time-dependent convection-diffusion-reaction problem in 2D. The suggested operator splitting approach divides the original model problem into two subproblems each in 1D, then solving each subproblem using WG-FEM in spatial direction eventually reduces the computational difficulty and high storage requirements. Backward Euler scheme is used for temporal derivative. Stability of the fully-discrete scheme has been studied and ε-uniform error estimates have been established. Numerical examples are provided validating our theoretical findings.