An efficient uniformly convergent method for multi-scaled two dimensional parabolic singularly perturbed systems of convection-diffusion type

Date

2025-01-01

Authors

Director

Publisher

Elsevier
Acceso abierto / Sarbide irekia
Artículo / Artikulua
Versión publicada / Argitaratu den bertsioa

Project identifier

  • AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2022-136441NB-I00/ES/ recolecta
  • AEI//TED2021-130884B-I00/
Impacto
OpenAlexGoogle Scholar
No disponible en Scopus

Abstract

In this work we solve initial-boundary value problems associated to coupled 2D parabolic singularly perturbed systems of convection-diffusion type. The analysis is focused on the cases where the diffusion parameters are small, distinct and also they may have different order of magnitude. In such cases, overlapping regular boundary layers appear at the outflow boundary of the spatial domain. The fully discrete scheme combines the classical upwind scheme defined on an appropriate Shishkin mesh to discretize the spatial variables, and the fractional implicit Euler method joins to a decomposition of the difference operator in directions and components to integrate in time. We prove that the resulting method is uniformly convergent of first order in time and of almost first order in space. Moreover, as only small tridiagonal linear systems must be solved to advance in time, the computational cost of our method is remarkably smaller than the corresponding ones to other implicit methods considered in the previous literature for the same type of problems. The numerical results, obtained for some test problems, corroborate in practice the good behavior and the advantages of the algorithm.

Description

Keywords

2D linear parabolic systems, Computational cost, Fractional implicit methods, Shishkin meshes, Splitting, Uniform convergence

Department

Estadística, Informática y Matemáticas / Estatistika, Informatika eta Matematika / Institute of Smart Cities - ISC

Faculty/School

Degree

Doctorate program

item.page.cita

Clavero, C., Jorge, J. C. (2025). An efficient uniformly convergent method for multi-scaled two dimensional parabolic singularly perturbed systems of convection-diffusion type. Applied Numerical Mathematics, 207, 174-192. https://doi.org/10.1016/j.apnum.2024.09.002.

item.page.rights

© 2024 The Author(s). This is an open access article under the CC BY-NC-ND license.

Licencia

Los documentos de Academica-e están protegidos por derechos de autor con todos los derechos reservados, a no ser que se indique lo contrario.