An efficient weak Galerkin FEM for third-order singularly perturbed convection-diffusion differential equations on layer-adapted meshes

TOPRAKSEVEN Ş., Srinivasan N.

Applied Numerical Mathematics, cilt.204, ss.130-146, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 204
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1016/j.apnum.2024.06.009
  • Dergi Adı: Applied Numerical Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Compendex, Computer & Applied Sciences, INSPEC, MathSciNet, zbMATH, DIALNET
  • Sayfa Sayıları: ss.130-146
  • Anahtar Kelimeler: Layer-adapted meshes, Third-order singularly perturbed problem, Uniform convergence, Weak Galerkin finite element scheme
  • Yozgat Bozok Üniversitesi Adresli: Evet

Özet

In this article, we study the weak Galerkin finite element method to solve a class of a third order singularly perturbed convection-diffusion differential equations. Using some knowledge on the exact solution, we prove a robust uniform convergence of order O(N−(k−1/2)) on the layer-adapted meshes including Bakhvalov-Shishkin type, and Bakhvalov-type and almost optimal uniform error estimates of order O((N−1ln⁡N)(k−1/2)) on Shishkin-type mesh with respect to the perturbation parameter in the energy norm using high-order piecewise discontinuous polynomials of degree k. Here N is the number mesh intervals. We conduct numerical examples to support our theoretical results.