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 dc.creator López García, José Luis dc.creator Pérez Sinusía, Ester dc.date.accessioned 2016-02-19T08:12:42Z dc.date.available 2016-02-19T08:12:42Z dc.date.issued 2007-09 dc.identifier.citation López García, J.L. y Pérez Sinusía, E. (2007). Asymptotic behaviour of a singularly perturbed convection-diffusion problem in a rectangle with discontinuous Dirichlet data. dc.identifier.uri http://hdl.handle.net/11441/35802 dc.description.abstract We consider a singularly perturbed convection-diffusion equation, −ε△u+ es −→v · −→∇u = 0, defined on a rectangular domain Ω ≡ {(x, y)| 0 ≤ x ≤ πa, 0 ≤ y ≤ π}, a > 0, with Dirichlet-type boundary conditions discontinuous at the points (0, 0) and (πa, 0): u(x, 0) = 1, u(x, π) = u(0, y) = u(πa, y) = 0. An asymptotic expansion of the solution is obtained from a a series representation in two limits: a) when the singular parameter ε → 0 + (with fixed distance to the points (0, 0) and (πa, 0)) and b) when (x, y) → (0, 0) or (x, y) → (πa, 0) (with fixed ε). It is shown that the first term of the expansion at ε = 0 contains a linear combination of error functions. This term characterizes the effect of the discontinuities on the ε−behaviour of the solution u(x, y) in the boundary or the internal layers. On the other hand, near the points of discontinuity (0, 0) and (πa, 0), the solution u(x, y) is approximated by a linear function of the polar angle. dc.format application/pdf es dc.language.iso eng es dc.relation.ispartof . dc.rights Attribution-NonCommercial-NoDerivatives 4.0 Internacional * dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/4.0/ * dc.subject Singular perturbation problem es dc.subject discontinuous boundary data es dc.subject asymptotic expansions es dc.subject error function es dc.title Asymptotic behaviour of a singularly perturbed convection-diffusion problem in a rectangle with discontinuous Dirichlet data es dc.type info:eu-repo/semantics/conferenceObject es dc.type.version info:eu-repo/semantics/publishedVersion es dc.rights.accessrights info:eu-repo/semantics/openAccess dc.identifier.idus https://idus.us.es/xmlui/handle/11441/35802
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