Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition

Gracia J.L. (Universidad de Zaragoza) ; O’Riordan E.

Resumen: A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the discontinuity in the initial condition and also satisfies the homogenous parabolic differential equation associated with the problem. The difference between this analytical function and the solution of the parabolic problem is approximated numerically, using an upwind finite difference operator combined with an appropriate layer-adapted mesh. The numerical method is shown to be parameter-uniform. Numerical results are presented to illustrate the theoretical error bounds established in the paper. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Idioma: Inglés

DOI: 10.1007/s11075-021-01098-6

Año: 2021

Publicado en: NUMERICAL ALGORITHMS 88, 4 (2021), 1851-1873
ISSN: 1017-1398

Factor impacto JCR: 2.37 (2021)

Categ. JCR: MATHEMATICS, APPLIED rank: 52 / 267 = 0.195 (2021) - Q1 - T1

Factor impacto CITESCORE: 4.7 - Mathematics (Q1)

Factor impacto SCIMAGO: 0.983 - Applied Mathematics (Q1)

Tipo y forma: Artículo (PrePrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)