Asymptotic approximations for a singularly perturbed convection-diffusion problem with discontinuous data in a sector

Authors:
José L. López;Ester Pérez Sinusía
Affiliations:
Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain;Departamento de Matemática e Informática, Universidad Pública de Navarra, 31006-Pamplona, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

Citing 3
Cited 1

Asymptotic expansions of symmetric standard elliptic integrals

SIAM Journal on Mathematical Analysis
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions

Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions

Analytical methods for an elliptic singular perturbation problem in a circle

Journal of Computational and Applied Mathematics

Quantified Score

Hi-index	7.29

Visualization

Abstract

We consider a singularly perturbed convection-diffusion equation, -@e@Du+v-.@?-u=0 on an arbitrary sector shaped domain, @W={(r,@f)|r0,00^+ (with fixed distance r to the discontinuity point of the boundary condition) and (b) when that distance r-0^+ (with fixed @e). It is shown that the first term of the expansion at @e=0 contains an error function. This term characterizes the effect of the discontinuity on the @e-behaviour of the solution and its derivatives in the boundary or internal layers. On the other hand, near discontinuity of the boundary condition r=0, the solution u(r,@f) of the problem is approximated by a linear function of the polar angle @f.