Adaptive numerical schemes for a parabolic problem with blow-up

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 r...

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Autores principales: Ferreira, R., Groisman, P., Rossi, J.D.
Formato: JOUR
Materias:
Adaptive mesh
Heat equation
Nonlinear boundary conditions
Numerical blow-up
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_02724979_v23_n3_p439_Ferreira
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_02724979_v23_n3_p439_Ferreira2023-10-03T15:15:16Z Adaptive numerical schemes for a parabolic problem with blow-up Ferreira, R. Groisman, P. Rossi, J.D. Adaptive mesh Heat equation Nonlinear boundary conditions Numerical blow-up 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. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Rossi, J.D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_02724979_v23_n3_p439_Ferreira
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Adaptive mesh
Heat equation
Nonlinear boundary conditions
Numerical blow-up
spellingShingle Adaptive mesh
Heat equation
Nonlinear boundary conditions
Numerical blow-up
Ferreira, R.
Groisman, P.
Rossi, J.D.
Adaptive numerical schemes for a parabolic problem with blow-up
topic_facet Adaptive mesh
Heat equation
Nonlinear boundary conditions
Numerical blow-up
description 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.
format JOUR
author Ferreira, R.
Groisman, P.
Rossi, J.D.
author_facet Ferreira, R.
Groisman, P.
Rossi, J.D.
author_sort Ferreira, R.
title Adaptive numerical schemes for a parabolic problem with blow-up
title_short Adaptive numerical schemes for a parabolic problem with blow-up
title_full Adaptive numerical schemes for a parabolic problem with blow-up
title_fullStr Adaptive numerical schemes for a parabolic problem with blow-up
title_full_unstemmed Adaptive numerical schemes for a parabolic problem with blow-up
title_sort adaptive numerical schemes for a parabolic problem with blow-up
url http://hdl.handle.net/20.500.12110/paper_02724979_v23_n3_p439_Ferreira
work_keys_str_mv AT ferreirar adaptivenumericalschemesforaparabolicproblemwithblowup
AT groismanp adaptivenumericalschemesforaparabolicproblemwithblowup
AT rossijd adaptivenumericalschemesforaparabolicproblemwithblowup
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