A Novel ADI-Weak Galerkin Method for Singularly Perturbed Two-Parameter 2D Parabolic Pdes

Raina A., Natesan S., TOPRAKSEVEN Ş.

Numerical Methods for Partial Differential Equations, vol.41, no.1, 2025 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 41 Issue: 1
  • Publication Date: 2025
  • Doi Number: 10.1002/num.23169
  • Journal Name: Numerical Methods for Partial Differential Equations
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: ADI-type method, convergence analysis, operator-splitting method, piecewise-uniform shishkin mesh, singularly perturbed 2D parabolic convection-reaction-diffusion problem, stability, WG-FEM
  • Yozgat Bozok University Affiliated: Yes

Abstract

In this article, we propose an Alternating Direction Implicit (ADI) type operator splitting weak Galerkin finite element method (WG-FEM) for solving a parabolic singularly perturbed problem with two-parameters in 2D over a layer-adapted mesh. The suggested operator splitting approach divides the original model problem into two subproblems each in 1D, then solving each subproblem using WG-FEM in spatial direction eventually reduces the computational difficulty and high storage requirements. Backward–Euler time discretization has been taken over a uniform mesh. Stability and convergence results have been proved for the fully-discrete scheme. Numerical examples are presented corroborating in practice our theoretical findings.