A Dimensionally Reduced Weak Galerkin FEM for Solving 2D Multi-Term Time-Fractional Diffusion Equation

Seal A., Natesan S., TOPRAKSEVEN Ş.

Numerical Methods for Partial Differential Equations, cilt.41, sa.5, 2025 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41 Sayı: 5
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/num.70024
  • Dergi Adı: Numerical Methods for Partial Differential Equations
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Anahtar Kelimeler: dimensional-reducing method, error analysis, multi-term time-fractional diffusion, numerical experiments, stability, weak Galerkin finite element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

This article presents a weak Galerkin finite element method combined with a dimensional-reduction strategy to numerically address a class of two-dimensional multi-term time-fractional diffusion equations. The temporal fractional derivative is discretized using the widely recognized non-uniform (Formula presented.) scheme, which is particularly effective in managing the singular behavior of integer-order temporal derivatives of the solution near the initial time. To handle spatial discretization, we adopt the dimensionally reduced weak Galerkin finite element method. This technique solves the problem sequentially along both spatial axes using a uniform mesh. The stability analysis is presented, and the optimal error estimates are derived in the (Formula presented.) norm. Lastly, numerical experiments are performed to confirm the theoretical findings and illustrate the effectiveness of the suggested approach.