A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes

TOPRAKSEVEN Ş., Dinibutun S.

Electronic Research Archive, vol.32, no.8, pp.5033-5066, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 32 Issue: 8
  • Publication Date: 2024
  • Doi Number: 10.3934/era.2024232
  • Journal Name: Electronic Research Archive
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5033-5066
  • Keywords: layer-adapted-meshes, semi-discrete and fully discrete schemes, time dependent singularly perturbed problem, weak Galerkin method
  • Yozgat Bozok University Affiliated: Yes

Abstract

In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.