000061426 001__ 61426
000061426 005__ 20190709135418.0
000061426 0247_ $$2doi$$a10.1016/j.cam.2015.10.031
000061426 0248_ $$2sideral$$a92738
000061426 037__ $$aART-2017-92738
000061426 041__ $$aeng
000061426 100__ $$0(orcid)0000-0003-1263-1996$$aClavero, C.$$uUniversidad de Zaragoza
000061426 245__ $$aAn efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers
000061426 260__ $$c2017
000061426 5060_ $$aAccess copy available to the general public$$fUnrestricted
000061426 5203_ $$aIn this paper we consider a 1D parabolic singularly perturbed reaction-convection-diffusion problem, which has a small parameter in both the diffusion term (multiplied by the parameter e2) and the convection term (multiplied by the parameter µ) in the differential equation (e¿(0, 1], µ¿0, 1], µ=e). Moreover, the convective term degenerates inside the spatial domain, and also the source term has a discontinuity of first kind on the degeneration line. In general, for sufficiently small values of the diffusion and the convection parameters, the exact solution exhibits an interior layer in a neighborhood of the interior degeneration point and also a boundary layer in a neighborhood of both end points of the spatial domain. We study the asymptotic behavior of the exact solution with respect to both parameters and we construct a monotone finite difference scheme, which combines the implicit Euler method, defined on a uniform mesh, to discretize in time, together with the classical upwind finite difference scheme, defined on an appropriate nonuniform mesh of Shishkin type, to discretize in space. The numerical scheme converges in the maximum norm uniformly in e and µ, having first order in time and almost first order in space. Illustrative numerical results corroborating in practice the theoretical results are showed.
000061426 536__ $$9info:eu-repo/grantAgreement/ES/UZ/CUD2014-CIE-09$$9info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859$$9info:eu-repo/grantAgreement/ES/MICINN/MTM2013-40842-P
000061426 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
000061426 590__ $$a1.632$$b2017
000061426 591__ $$aMATHEMATICS, APPLIED$$b49 / 252 = 0.194$$c2017$$dQ1$$eT1
000061426 592__ $$a0.938$$b2017
000061426 593__ $$aComputational Mathematics$$c2017$$dQ2
000061426 593__ $$aApplied Mathematics$$c2017$$dQ2
000061426 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/submittedVersion
000061426 700__ $$0(orcid)0000-0003-2538-9027$$aGracia, J.L.$$uUniversidad de Zaragoza
000061426 700__ $$aShishkin, G. I.
000061426 700__ $$aShishkina, L.P.
000061426 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000061426 773__ $$g318 (2017), 634-645$$pJ. comput. appl. math.$$tJournal of Computational and Applied Mathematics$$x0377-0427
000061426 8564_ $$s409969$$uhttps://zaguan.unizar.es/record/61426/files/texto_completo.pdf$$yPreprint
000061426 8564_ $$s69824$$uhttps://zaguan.unizar.es/record/61426/files/texto_completo.jpg?subformat=icon$$xicon$$yPreprint
000061426 909CO $$ooai:zaguan.unizar.es:61426$$particulos$$pdriver
000061426 951__ $$a2019-07-09-11:24:57
000061426 980__ $$aARTICLE