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Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems

Author

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  • Raina, Aayushman
  • Natesan, Srinivasan
  • Toprakseven, Şuayip

Abstract

We consider the weak Galerkin finite element approximation of the singularly perturbed biharmonic elliptic problem on a unit square domain with clamped boundary conditions. Shishkin mesh is used for domain discretization as the solution exhibits boundary layers near the domain boundary. Error estimates in the equivalent H2− norm have been established and the uniform convergence of the proposed method has been proved. Numerical examples are presented corroborating our theoretical findings.

Suggested Citation

  • Raina, Aayushman & Natesan, Srinivasan & Toprakseven, Şuayip, 2025. "Anisotropic error analysis of weak Galerkin finite element method for singularly perturbed biharmonic problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 203-221.
    • Handle: RePEc:eee:matcom:v:229:y:2025:i:c:p:203-221
    DOI: 10.1016/j.matcom.2024.09.017
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    References listed on IDEAS

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    1. Zhang, J. & Liu, X., 2022. "Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Zhang, Jin & Liu, Xiaowei, 2022. "Uniform convergence of a weak Galerkin method for singularly perturbed convection–diffusion problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 393-403.
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    1. Zhang, J. & Liu, X., 2022. "Uniform convergence of a weak Galerkin finite element method on Shishkin mesh for singularly perturbed convection-diffusion problems in 2D," Applied Mathematics and Computation, Elsevier, vol. 432(C).

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