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Convergence analysis of a fully-discrete FEM for singularly perturbed two-parameter parabolic PDE

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  • Avijit, D.
  • Natesan, S.

Abstract

This article deals with the numerical solution of a singularly perturbed initial–boundary value problem (IBVP) with two parameters on a rectangular space–time domain. A fully-discrete numerical method by combining the Crank–Nicolson scheme for temporal derivative and the streamline-diffusion finite element method (SDFEM) for spatial derivatives has been established in a new theoretical framework. A suitable stabilization parameter has been explored on some conditions related to error analysis. The robust error estimates and the stability results are obtained by using P1-finite element in the discrete L2(0,T;SD)-norm. Theoretical results are verified by some numerical experiments.

Suggested Citation

  • Avijit, D. & Natesan, S., 2022. "Convergence analysis of a fully-discrete FEM for singularly perturbed two-parameter parabolic PDE," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 185-206.
    • Handle: RePEc:eee:matcom:v:197:y:2022:i:c:p:185-206
    DOI: 10.1016/j.matcom.2022.02.005
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