Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9509563 | Journal of Computational and Applied Mathematics | 2005 | 23 Pages |
Abstract
We consider a singularly perturbed convection-diffusion equation, -εÎu+vâ·ââu=0 on an arbitrary sector shaped domain, Ωâ¡{(r,Ï)|r>0,0<Ï<α} being r and Ï polar coordinates and 0<α<2Ï. We consider for this problem discontinuous Dirichlet boundary conditions at the corner of the sector: u(r,0)=0,u(r,α)=1. An asymptotic expansion of the solution is obtained from an integral representation in two limits: (a) when the singular parameter εâ0+ (with fixed distance r to the discontinuity point of the boundary condition) and (b) when that distance râ0+ (with fixed ε). It is shown that the first term of the expansion at ε=0 contains an error function. This term characterizes the effect of the discontinuity on the ε-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,Ï) of the problem is approximated by a linear function of the polar angle Ï.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
José L. López, Ester Pérez SinusÃa,