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<p>In this paper, we have introduced an operator splitting weak Galerkin finite element method (WG-FEM) for a class of second order singularly perturbed time-dependent convection-diffusion-reaction problem in 2D. 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 scheme is used for temporal derivative. Stability of the fully-discrete scheme has been studied and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-uniform error estimates have been established. Numerical examples are provided validating our theoretical findings.</p>

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An efficient operator splitting weak Galerkin method for singularly perturbed 2D parabolic PDEs

  • 期刊论文

  • 发表日期：

    2025年7月1日

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  • Aayushman Raina,
  • Srinivasan Natesan,
  • Şuayip Toprakseven

摘要

In this paper, we have introduced an operator splitting weak Galerkin finite element method (WG-FEM) for a class of second order singularly perturbed time-dependent convection-diffusion-reaction problem in 2D. 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 scheme is used for temporal derivative. Stability of the fully-discrete scheme has been studied and \(\varepsilon \) ε -uniform error estimates have been established. Numerical examples are provided validating our theoretical findings.