About: A posteriori estimates and stopping criteria for iterative linearizations and linear solvers

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We present the a posteriori error estimates which enable to take into account the linearization error in approximation of nonlinear problems and the algebraic error in the solution of linear systems associated to the given numerical discretization. Our estimates allow to distinguish, estimate separately, and compare these different error sources. Consequently, the iterative (Newton, quasi-Newton) linearization or iterative solution of linear algebraic systems can be stopped whenever the individual errors drop to the level at which they do not affect significantly the overall error. This can lead to important computational savings, as performing an excessive number of unnecessary linearization/linear solver iterations can be avoided. Moreover, due to their local efficiency, our estimators also allow to accurately predict the error spatial distribution and thus they are suitable for local adaptive mesh refinement. Finally, they give a fully computable upper bound on the overall error. This allows to devise an adaptive strategy enabling to achieve a user-given precision at minimal cost. Numerical experiments illustrate the theoretical developments. We present the a posteriori error estimates which enable to take into account the linearization error in approximation of nonlinear problems and the algebraic error in the solution of linear systems associated to the given numerical discretization. Our estimates allow to distinguish, estimate separately, and compare these different error sources. Consequently, the iterative (Newton, quasi-Newton) linearization or iterative solution of linear algebraic systems can be stopped whenever the individual errors drop to the level at which they do not affect significantly the overall error. This can lead to important computational savings, as performing an excessive number of unnecessary linearization/linear solver iterations can be avoided. Moreover, due to their local efficiency, our estimators also allow to accurately predict the error spatial distribution and thus they are suitable for local adaptive mesh refinement. Finally, they give a fully computable upper bound on the overall error. This allows to devise an adaptive strategy enabling to achieve a user-given precision at minimal cost. Numerical experiments illustrate the theoretical developments. (en)
Title	A posteriori estimates and stopping criteria for iterative linearizations and linear solvers A posteriori estimates and stopping criteria for iterative linearizations and linear solvers (en)
skos:prefLabel	A posteriori estimates and stopping criteria for iterative linearizations and linear solvers A posteriori estimates and stopping criteria for iterative linearizations and linear solvers (en)
skos:notation	RIV/00216208:11320/11:10107093!RIV12-GA0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/0917), Z(MSM0021620839)
http://linked.open...vai/riv/dodaniDat	2012
http://linked.open...aciTvurceVysledku	Strakoš, Zdeněk
http://linked.open.../riv/druhVysledku	D - Článek ve sborníku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	184063
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/11:10107093
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	stopping criteria; a posteriori error estimate; iterative methods; linearization; finite volume method; nonlinear problem (en)
http://linked.open.../riv/klicoveSlovo	finite volume method linearization a posteriori error estimate iterative methods nonlinear problem stopping criteria
http://linked.open...ontrolniKodProRIV	[6546E83A9F09]
http://linked.open...v/mistoKonaniAkce	Liberec
http://linked.open...i/riv/mistoVydani	Liberec
http://linked.open...i/riv/nazevZdroje	International Conference Presentation of Mathematics '10
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	5 (xsd:int)
http://linked.open...vavai/riv/projekt	Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials
http://linked.open...UplatneniVysledku	2011
http://linked.open...iv/tvurceVysledku	El Alaoui, Linda Ern, Alexandre Jiránek, Pavel Strakoš, Zdeněk Vohralík, Martin
http://linked.open...vavai/riv/typAkce	EUR - Evropská
http://linked.open.../riv/zahajeniAkce	2010-10-21 (xsd:date)
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
number of pages	8 (xsd:int)
http://purl.org/ne...btex#hasPublisher	TU Liberec
https://schema.org/isbn	978-80-7372-724-6
http://localhost/t...ganizacniJednotka	11320

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