Superconvergence of a modified weak Galerkin method for singularly perturbed two-point elliptic boundary-value problems

Toprakseven Ş.

Calcolo, cilt.59, sa.1, 2022 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2022
  • Doi Numarası: 10.1007/s10092-021-00449-y
  • Dergi Adı: Calcolo
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Convection–reaction–diffusion, Layer adapted Shishkin mesh, Reaction–diffusion, Singularly perturbed, Superconvergence, The modified weak Galerkin finite element method
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

In this paper, superconvergence approximations of the modified weak Galerkin finite element method for the singularly perturbed two-point elliptic boundary-value problem have been studied. On the piecewise uniform Shishkin mesh, we have established the superconvergence error bounds of O(N-1lnN)k+1 in the discrete energy norm, where k is the degree of polynomials used in the finite element space and N is the number of elements. Stability analyses have been carried out for both singularly perturbed reaction–diffusion and convection-dominated problems. Some numerical examples are presented to support the theoretical findings. Moreover, the numerical experiments show that the proposed method has the superconvergence error bounds of O(N-1lnN)2k in the discrete L∞-norm.