Mukherjee, Kaushik; Natesan, Srinivasan Optimal error estimate of upwind scheme on Shishkin-type meshes for singularly perturbed parabolic problems with discontinuous convection coefficients. (English) Zbl 1230.65104 BIT 51, No. 2, 289-315 (2011). A class of singularly perturbed parabolic convection-diffusion problems with discontinuous convection coefficient is considered. Due to the discontinuity of this coefficient the solution possesses interior layers. The analysis of an implicit upwind finite difference scheme on both piecewise-uniform Shishkin mesh and the Bakhalov-Shishkin mesh, for the considered problem, is performed. The authors derive suitable conditions for the appropriate mesh-generating functions which are sufficient for the convergence of the method, uniformly with respect to the perturbation parameter. It is proved from a theoretical and from a numerical point of view as well that the scheme converges uniformly in the discrete supremum norm with an optimal error bound. Reviewer: Ruxandra Stavre (Bucureşti) Cited in 9 Documents MSC: 65M15 Error bounds for initial value and initial-boundary value problems involving PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K20 Initial-boundary value problems for second-order parabolic equations 35B25 Singular perturbations in context of PDEs 65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs Keywords:singular perturbation; interior layer; Shishkin-type meshes; uniform convergence; parabolic convection-diffusion problems; discontinuous convection coefficient; implicit upwind finite difference scheme; Bakhalov-Shishkin mesh; mesh-generating functions; optimal error bound PDFBibTeX XMLCite \textit{K. Mukherjee} and \textit{S. 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