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

D. Avijit and S. Natesan

Mathematics and Computers in Simulation (MATCOM), 2022, vol. 197, issue C, 185-206

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.

Keywords: Singularly perturbed 1D two-parameter parabolic PDEs; Streamline-diffusion finite element method; Bakhvalov-type mesh; Shishkin mesh; Exponentially graded mesh; Stability; Error analysis (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:197:y:2022:i:c:p:185-206

DOI: 10.1016/j.matcom.2022.02.005

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