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Abstract:

In this paper we present adaptive procedures for the numerical study of positive solutions of the following problem: {ut = uxx (x,t) ∈ (0, 1) × [0, T), ux (0, t) = 0 t ∈ [0, T), ux (1, t) = up (1, t) t ∈ [0, T), u(x, 0) = u 0(x) x ∈ (0, 1), with p > 1. We describe two methods. The first one refines the mesh in the region where the solution becomes bigger in a precise way that allows us to recover the blow-up rate and the blow-up set of the continuous problem. The second one combines the ideas used in the first one with moving mesh methods and moves the last points when necessary. This scheme also recovers the blow-up rate and set. Finally, we present numerical experiments to illustrate the behaviour of both methods.

Registro:

Documento: Artículo
Título:Adaptive numerical schemes for a parabolic problem with blow-up
Autor:Ferreira, R.; Groisman, P.; Rossi, J.D.
Filiación:Depto. de Matemáticas, U. Autónoma de Madrid, 28049 Madrid, Spain
Depto. de Matemática, FCEyN., UBA, 1428 Buenos Aires, Argentina
Depto de Matematica, Pont. Universidad, Catolica de Chile, Casilla 306, Correo 22, Santiago, Chile
Palabras clave:Adaptive mesh; Heat equation; Nonlinear boundary conditions; Numerical blow-up
Año:2003
Volumen:23
Número:3
Página de inicio:439
Página de fin:463
DOI: http://dx.doi.org/10.1093/imanum/23.3.439
Título revista:IMA Journal of Numerical Analysis
Título revista abreviado:IMA J. Numer. Anal.
ISSN:02724979
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02724979_v23_n3_p439_Ferreira

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Citas:

---------- APA ----------
Ferreira, R., Groisman, P. & Rossi, J.D. (2003) . Adaptive numerical schemes for a parabolic problem with blow-up. IMA Journal of Numerical Analysis, 23(3), 439-463.
http://dx.doi.org/10.1093/imanum/23.3.439
---------- CHICAGO ----------
Ferreira, R., Groisman, P., Rossi, J.D. "Adaptive numerical schemes for a parabolic problem with blow-up" . IMA Journal of Numerical Analysis 23, no. 3 (2003) : 439-463.
http://dx.doi.org/10.1093/imanum/23.3.439
---------- MLA ----------
Ferreira, R., Groisman, P., Rossi, J.D. "Adaptive numerical schemes for a parabolic problem with blow-up" . IMA Journal of Numerical Analysis, vol. 23, no. 3, 2003, pp. 439-463.
http://dx.doi.org/10.1093/imanum/23.3.439
---------- VANCOUVER ----------
Ferreira, R., Groisman, P., Rossi, J.D. Adaptive numerical schemes for a parabolic problem with blow-up. IMA J. Numer. Anal. 2003;23(3):439-463.
http://dx.doi.org/10.1093/imanum/23.3.439