About: A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1137/110859282
Description	We derive a framework for a posteriori error estimates in unsteady, nonlinear, possibly degenerate, advection-diffusion problems. Our estimators are based on a space-time equilibrated flux reconstruction and are locally computable. They are derived for the error measured in a space-time mesh-dependent dual norm stemming from the problem and meshes at hand augmented by a jump seminorm measuring possible nonconformities in space. Owing to this choice, a guaranteed and globally efficient upper bound is achieved, as well as robustness with respect to nonlinearities, advection dominance, domain size, final time, and absolute and relative size of space and time steps. Local-in-time and in-space efficiency is also shown for a localized upper bound of the error measure. In order to apply the framework to a given numerical method, two simple conditions, local space-time mass conservation and an approximation property of the reconstructed fluxes, need to be verified. We show how to do this for the interior-penalty discontinuous Galerkin method in space and the Crank-Nicolson scheme in time. Numerical experiments illustrate the theory. We derive a framework for a posteriori error estimates in unsteady, nonlinear, possibly degenerate, advection-diffusion problems. Our estimators are based on a space-time equilibrated flux reconstruction and are locally computable. They are derived for the error measured in a space-time mesh-dependent dual norm stemming from the problem and meshes at hand augmented by a jump seminorm measuring possible nonconformities in space. Owing to this choice, a guaranteed and globally efficient upper bound is achieved, as well as robustness with respect to nonlinearities, advection dominance, domain size, final time, and absolute and relative size of space and time steps. Local-in-time and in-space efficiency is also shown for a localized upper bound of the error measure. In order to apply the framework to a given numerical method, two simple conditions, local space-time mass conservation and an approximation property of the reconstructed fluxes, need to be verified. We show how to do this for the interior-penalty discontinuous Galerkin method in space and the Crank-Nicolson scheme in time. Numerical experiments illustrate the theory. (en)
Title	A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS (en)
skos:prefLabel	A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS (en)
skos:notation	RIV/00216208:11320/13:10159214!RIV14-GA0-11320___
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA201/08/0012)
http://linked.open...iv/cisloPeriodika	2
http://linked.open...vai/riv/dodaniDat	2014
http://linked.open...aciTvurceVysledku	Dolejší, Vít
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	58619
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/13:10159214
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	discontinuous Galerkin method; robustness; unified framework; flux equilibration; flux reconstruction; dual norm; a posteriori estimate; unsteady nonlinear advection-diffusion problem (en)
http://linked.open.../riv/klicoveSlovo	a posteriori estimate dual norm flux equilibration flux reconstruction unified framework unsteady nonlinear advection-diffusion problem discontinuous Galerkin method robustness
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[5A11973CDAA9]
http://linked.open...i/riv/nazevZdroje	SIAM Journal on Numerical Analysis
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	Qualitative analysis and numerical solution of flow problems
http://linked.open...UplatneniVysledku	2013
http://linked.open...v/svazekPeriodika	51
http://linked.open...iv/tvurceVysledku	Dolejší, Vít Ern, Alexandre Vohralik, Martin
http://linked.open...ain/vavai/riv/wos	000318405100002
issn	0036-1429
number of pages	21 (xsd:int)
http://bibframe.org/vocab/doi	10.1137/110859282
http://localhost/t...ganizacniJednotka	11320

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