About: Verification of functional a posteriori error estimates for obstacle problem in 2D

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value contains three unknown fields: a gradient field discretized by Raviart–Thomas elements, Lagrange multipliers field discretized by piecewise constant functions and a scalar parameter β. The minimization of the majorant value is realized by an alternate minimization algorithm, whose convergence is discussed. Numerical results validate two estimates, the energy estimate bounding the error of approximation in the energy norm by the difference of energies of discrete and exact solutions and the majorant estimate bounding the difference of energies of discrete and exact solutions by the value of the functional majorant. We verify functional a posteriori error estimates proposed by S. Repin for a class of obstacle problems in two space dimensions. New benchmarks with known analytical solution are constructed based on one dimensional benchmark introduced by P. Harasim and J. Valdman. Numerical approximation of the solution of the obstacle problem is obtained by the finite element method using bilinear elements on a rectangular mesh. Error of the approximation is measured by a functional majorant. The majorant value contains three unknown fields: a gradient field discretized by Raviart–Thomas elements, Lagrange multipliers field discretized by piecewise constant functions and a scalar parameter β. The minimization of the majorant value is realized by an alternate minimization algorithm, whose convergence is discussed. Numerical results validate two estimates, the energy estimate bounding the error of approximation in the energy norm by the difference of energies of discrete and exact solutions and the majorant estimate bounding the difference of energies of discrete and exact solutions by the value of the functional majorant. (en)
Title	Verification of functional a posteriori error estimates for obstacle problem in 2D Verification of functional a posteriori error estimates for obstacle problem in 2D (en)
skos:prefLabel	Verification of functional a posteriori error estimates for obstacle problem in 2D Verification of functional a posteriori error estimates for obstacle problem in 2D (en)
skos:notation	RIV/67985556:_____/14:00441661!RIV15-GA0-67985556
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GA13-18652S)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2015
http://linked.open...aciTvurceVysledku	Valdman, Jan
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	Ústav teorie informace a automatizace AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	53234
http://linked.open...ai/riv/idVysledku	RIV/67985556:_____/14:00441661
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	obstacle problem; a posteriori error estimate; finite element method; variational inequalities (en)
http://linked.open.../riv/klicoveSlovo	variational inequalities finite element method a posteriori error estimate obstacle problem
http://linked.open...odStatuVydavatele	CZ - Česká republika
http://linked.open...ontrolniKodProRIV	[CF37D6AFE741]
http://linked.open...i/riv/nazevZdroje	Kybernetika
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Numerické modelování poškození a transportních procesů v kvazikřehkých materiálech
http://linked.open...UplatneniVysledku	2014
http://linked.open...v/svazekPeriodika	50
http://linked.open...iv/tvurceVysledku	Valdman, Jan Harasim, P.
http://linked.open...ain/vavai/riv/wos	000348961900008
issn	0023-5954
number of pages	25 (xsd:int)
http://bibframe.org/vocab/doi	10.14736/kyb-2014-6-0978

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