A numerical method for singularly perturbed convection–diffusion–reaction equations on polygonal meshes

Kumar N., Toprakseven Ş., Jiwari R.

Computational and Applied Mathematics, cilt.43, sa.1, 2024 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 43 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1007/s40314-023-02553-x
  • Dergi Adı: Computational and Applied Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Convection–diffusion–reaction equation, Optimal order, Polygonal meshes, Singular perturbation, Weak Galerkin method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

In this paper, we design and develop a weak Galerkin finite-element numerical method for solving singularly perturbed convection–diffusion–reaction equations with a non-conservation convection term. Many advantages of the proposed method include support for the higher order of convergence and general polygonal meshes. The convergence study for the weak Galerkin algorithm is performed in both the triple-bar norm and the L2 norm. We achieve an optimal order of convergence of O(hk) in the triple-bar norm and O(hk+1) in the L2 norm. Several numerical experiments in a two-dimensional setting are carried out to demonstrate the convergence of our theories.