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01.09.2017

A parameter-uniform second order numerical method for a weakly coupled system of singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms

Erschienen in: Calcolo | Ausgabe 3/2017

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Abstract

In this article, a parameter-uniform hybrid numerical method is presented to solve a weakly coupled system of two singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms. Due to these discontinuities, interior layers appear in the solution of the problem considered. The hybrid numerical method uses the standard finite difference scheme in the coarse mesh region and the cubic spline difference scheme in the fine mesh region which is constructed on piecewise-uniform Shishkin mesh. Second order one sided difference approximations are used at the point of discontinuity. Error analysis is carried out and the method ensures that the parameter-uniform convergence of almost the second order. Numerical results are provided to validate the theoretical results.

Vorheriger Artikel Discrete p-robust -liftings and a posteriori estimates for elliptic problems with source terms

Nächster Artikel A posteriori error analysis of an augmented mixed-primal formulation for the stationary Boussinesq model

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Titel: A parameter-uniform second order numerical method for a weakly coupled system of singularly perturbed convection–diffusion equations with discontinuous convection coefficients and source terms
Publikationsdatum: 01.09.2017
Erschienen in: Calcolo / Ausgabe 3/2017
Print ISSN: 0008-0624
Elektronische ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-017-0218-3

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