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Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms

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  • Toprakseven, Şuayip
  • Zhu, Peng

Abstract

A weak Galerkin finite element method is proposed for solving singularly perturbed problems with two parameters. A robust uniform optimal convergence has been proved in the corresponding energy and a stronger balanced norms using piecewise higher order discontinuous polynomials on a piecewise uniform Shishkin mesh. Finally, we give some numerical experiments to support theoretical results.

Suggested Citation

  • Toprakseven, Şuayip & Zhu, Peng, 2023. "Error analysis of a weak Galerkin finite element method for two-parameter singularly perturbed differential equations in the energy and balanced norms," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    • Handle: RePEc:eee:apmaco:v:441:y:2023:i:c:s0096300322007512
    DOI: 10.1016/j.amc.2022.127683
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    References listed on IDEAS

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    1. T. Valanarasu & N. Ramanujan, 2003. "Asymptotic Initial-Value Method for Singularly-Perturbed Boundary-Value Problems for Second-Order Ordinary Differential Equations," Journal of Optimization Theory and Applications, Springer, vol. 116(1), pages 167-182, January.
    2. Surla, K. & Uzelac, Z. & Teofanov, Lj., 2009. "The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2490-2505.
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