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A streamline-diffusion FEM for singularly perturbed degenerate parabolic problem with large delay argument

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  • Aasna,
  • Rai, Pratima

Abstract

This article considers a class of singularly perturbed degenerate parabolic problem of convection–diffusion type with large space delay argument. When the convection term dominates over the diffusion term, the solution displays strong boundary layers, while the presence of a delay argument produces a weak interior layer. An implicit finite-difference scheme based on a weighted θ-method is applied for time discretization on an equidistant mesh, and streamline-diffusion finite element method (SDFEM) is used for space discretization on layer-adapted generalized Shishkin mesh. In this study, we have addressed the challenges arising due to the presence of delay argument and degenerate coefficient. The parameter uniform convergence of the proposed method is obtained for the considered class of problems in the maximum norm. Several test problems are considered for the numerical validation and to demonstrate the efficiency of the proposed numerical scheme. Additionally, the solution plots are provided to better illustrate the effect of the delay term.

Suggested Citation

  • Aasna, & Rai, Pratima, 2026. "A streamline-diffusion FEM for singularly perturbed degenerate parabolic problem with large delay argument," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 247(C), pages 649-673.
    • Handle: RePEc:eee:matcom:v:247:y:2026:i:c:p:649-673
    DOI: 10.1016/j.matcom.2026.04.001
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    References listed on IDEAS

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    1. Das, Abhishek & Natesan, Srinivasan, 2015. "Uniformly convergent hybrid numerical scheme for singularly perturbed delay parabolic convection–diffusion problems on Shishkin mesh," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 168-186.
    2. V.Y. Glizer, 2003. "Asymptotic Analysis and Solution of a Finite-Horizon H ∞ Control Problem for Singularly-Perturbed Linear Systems with Small State Delay," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 295-325, May.
    3. Sharma, Amit & Rai, Pratima, 2023. "Analysis of a higher order uniformly convergent method for singularly perturbed parabolic delay problems," Applied Mathematics and Computation, Elsevier, vol. 448(C).
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