research-article

Numerical solution of singularly perturbed convection-diffusion-reaction problems with two small parameters

Authors:

Pratibhamoy Das,

Volker MehrmannAuthors Info & Claims

Volume 56, Issue 1

Pages 51 - 76

https://doi.org/10.1007/s10543-015-0559-8

Published: 01 March 2016 Publication History

Abstract

This paper discusses the numerical solution of linear 1-D singularly perturbed parabolic convection-diffusion-reaction problems with two small parameters using a moving mesh-adaptive algorithm which adapts meshes to boundary layers. The meshes are generated by the equidistribution of a special positive monitor function. Parameter independent uniform convergence is shown for a class of model problems and the obtained result hold even for the limiting case where the perturbation parameters are zero. Numerical experiments are presented that illustrate the first-order parameter uniform convergence, and also show that the new approach has better accuracy compared with current methods.

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Cited By

Kurina GKalashnikova M(2022)Singularly Perturbed Problems with Multi-Tempo Fast VariablesAutomation and Remote Control10.1134/S0005117922011001783:11(1679-1723)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1134/S00051179220110017
Zhou JYao XWang W(2022)Two-grid finite element methods for nonlinear time-fractional parabolic equationsNumerical Algorithms10.1007/s11075-021-01205-790:2(709-730)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s11075-021-01205-7
Antoine XLorin EZhang Y(2021)Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layersNumerical Algorithms10.1007/s11075-020-00972-z87:1(409-444)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11075-020-00972-z
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cover image BIT

BIT Volume 56, Issue 1

Mar 2016

388 pages

ISSN:0006-3835

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Copyright © 2016 Springer Science+Business Media Dordrecht.

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BIT Computer Science and Numerical Mathematics

United States

Publication History

Published: 01 March 2016

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Cited By

Kurina GKalashnikova M(2022)Singularly Perturbed Problems with Multi-Tempo Fast VariablesAutomation and Remote Control10.1134/S0005117922011001783:11(1679-1723)Online publication date: 1-Nov-2022
https://dl.acm.org/doi/10.1134/S00051179220110017
Zhou JYao XWang W(2022)Two-grid finite element methods for nonlinear time-fractional parabolic equationsNumerical Algorithms10.1007/s11075-021-01205-790:2(709-730)Online publication date: 1-Jun-2022
https://dl.acm.org/doi/10.1007/s11075-021-01205-7
Antoine XLorin EZhang Y(2021)Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layersNumerical Algorithms10.1007/s11075-020-00972-z87:1(409-444)Online publication date: 1-May-2021
https://dl.acm.org/doi/10.1007/s11075-020-00972-z
Zhai SWu LWang JWeng Z(2019)Numerical approximation of the fractional Cahn-Hilliard equation by operator splitting methodNumerical Algorithms10.1007/s11075-019-00795-784:3(1155-1178)Online publication date: 23-Aug-2019
https://dl.acm.org/doi/10.1007/s11075-019-00795-7

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