Alternating direction numerical scheme for singularly perturbed 2D degenerate parabolic convection-diffusion problems

Anirban Majumdar and Srinivasan Natesan

Applied Mathematics and Computation, 2017, vol. 313, issue C, 453-473

Abstract: In this article, we study the numerical solution of singularly perturbed 2D degenerate parabolic convection-diffusion problems on a rectangular domain. The solution of this problem exhibits parabolic boundary layers along x=0,y=0 and a corner layer in the neighborhood of (0, 0). First, we use an alternating direction implicit finite difference scheme to discretize the time derivative of the continuous problem on a uniform mesh in the temporal direction. Then, to discretize the spatial derivatives of the resulting time semidiscrete problems, we apply the upwind finite difference scheme on a piecewise-uniform Shishkin mesh. We derive error estimate for the proposed numerical scheme, which shows that the scheme is ε-uniformly convergent of almost first-order (up to a logarithmic factor) in space and first-order in time. Some numerical results have been carried out to validate the theoretical results.

Keywords: Singularly perturbed 2D degenerate parabolic convection-diffusion problem; Alternating direction scheme; Finite difference scheme; Piecewise-uniform Shishkin meshes; Uniform convergence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:453-473

DOI: 10.1016/j.amc.2017.06.010

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