About: Distribution of the discretization and algebraic error in numerical solution of partial differential equations

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About: Distribution of the discretization and algebraic error in numerical solution of partial differential equations Goto Sponge NotDistinct Permalink

An Entity of Type : http://linked.opendata.cz/ontology/domain/vavai/Vysledek, within Data Space : linked.opendata.cz associated with source document(s)

Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.laa.2014.02.009
Description	In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary value model problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is not restricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere. In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary value model problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is not restricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere. (en)
Title	Distribution of the discretization and algebraic error in numerical solution of partial differential equations Distribution of the discretization and algebraic error in numerical solution of partial differential equations (en)
skos:prefLabel	Distribution of the discretization and algebraic error in numerical solution of partial differential equations Distribution of the discretization and algebraic error in numerical solution of partial differential equations (en)
skos:notation	RIV/00216208:11320/14:10286559!RIV15-MSM-11320___
http://linked.open...avai/riv/aktivita	I P S
http://linked.open...avai/riv/aktivity	I, P(GA201/09/0917), P(IAA100300802), P(LL1202), S
http://linked.open...iv/cisloPeriodika	15 May 2014
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Strakoš, Zdeněk
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
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	11860
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/14:10286559
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Spatial distribution of the error; Algebraic error; Discretization error; A posteriori error analysis; Adaptivity; Finite element method; Numerical solution of partial differential equations (en)
http://linked.open.../riv/klicoveSlovo	A posteriori error analysis Discretization error Numerical solution of partial differential equations Spatial distribution of the error Finite element method Algebraic error Adaptivity
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[E31F00895510]
http://linked.open...i/riv/nazevZdroje	Linear Algebra and Its Applications
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	3 (xsd:int)
http://linked.open...vavai/riv/projekt	Theory of Krylov subspace methods and its relationship to other mathematical disciplines Mathematical and computer analysis of the evolution processes in nonlinear viscoelastic fluid-like materials Implicitly constituted material models: from theory through model reduction to efficient numerical methods
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	449
http://linked.open...iv/tvurceVysledku	Strakoš, Zdeněk Papež, Jan Liesen, J.
http://linked.open...ain/vavai/riv/wos	000336699600008
issn	0024-3795
number of pages	26 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.laa.2014.02.009
http://localhost/t...ganizacniJednotka	11320

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