000063083 001__ 63083
000063083 005__ 20220621094623.0
000063083 0247_ $$2doi$$a10.1007/s11075-016-0221-9
000063083 0248_ $$2sideral$$a96628
000063083 037__ $$aART-2017-96628
000063083 041__ $$aeng
000063083 100__ $$0(orcid)0000-0003-1263-1996$$aClavero, C.$$uUniversidad de Zaragoza
000063083 245__ $$aA fractional step method for 2D parabolic convection-diffusion singularly perturbed problems: uniform convergence and order reduction
000063083 260__ $$c2017
000063083 5060_ $$aAccess copy available to the general public$$fUnrestricted
000063083 5203_ $$aIn this work, we are concerned with the efficient resolution of two dimensional parabolic singularly perturbed problems of convection-diffusion type. The numerical method combines the fractional implicit Euler method to discretize in time on a uniform mesh and the classical upwind finite difference scheme, defined on a Shishkin mesh, to discretize in space. We consider general time-dependent Dirichlet boundary conditions, and we show that classical evaluations of the boundary conditions cause an order reduction in the consistency of the time integrator. An appropriate correction for the evaluations of the boundary data permits to remove such order reduction. Using this correction, we prove that the fully discrete scheme is uniformly convergent of first order in time and of almost first order in space. Some numerical experiments, which corroborate in practice the robustness and the efficiency of the proposed numerical algorithm, are shown; from them, we bring to light the influence in practice of the two options for the boundary data considered here, which is in agreement with the theoretical results.
000063083 536__ $$9info:eu-repo/grantAgreement/ES/MINECO/MTM2014-52859
000063083 540__ $$9info:eu-repo/semantics/openAccess$$aAll rights reserved$$uhttp://www.europeana.eu/rights/rr-f/
000063083 590__ $$a1.536$$b2017
000063083 591__ $$aMATHEMATICS, APPLIED$$b55 / 252 = 0.218$$c2017$$dQ1$$eT1
000063083 592__ $$a0.981$$b2017
000063083 593__ $$aApplied Mathematics$$c2017$$dQ2
000063083 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion
000063083 700__ $$aJorge, J. C.
000063083 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada
000063083 773__ $$g75, 3 (2017), 809-826$$pNumer. algorithms$$tNumerical Algorithms$$x1017-1398
000063083 8564_ $$s419875$$uhttps://zaguan.unizar.es/record/63083/files/texto_completo.pdf$$yPostprint
000063083 8564_ $$s53316$$uhttps://zaguan.unizar.es/record/63083/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint
000063083 909CO $$ooai:zaguan.unizar.es:63083$$particulos$$pdriver
000063083 951__ $$a2022-06-21-09:39:51
000063083 980__ $$aARTICLE