A posteriori error identities for nonlinear variational problems
Neittaanmäki, P., & Repin, S. (2015). A posteriori error identities for nonlinear variational problems. Annals of the Acacemy of Romanian Scientists : Mathematics and Its Applications, 7(1), 157-172. http://www.mathematics-and-its-applications.com/preview/june2015/data/articol10.pdf
Date
2015Copyright
© the Authors & Annals of the Acacemy of Romanian Scientists, 2015. This is an open access article published by Academy of Romanian Scientists.
A posteriori error estimation methods are usually developed in the
context of upper and lower bounds of errors. In this paper, we are concerned
with a posteriori analysis in terms of identities, i.e., we deduce
error relations, which holds as equalities. We discuss a general form
of error identities for a wide class of convex variational problems. The
left hand sides of these identities can be considered as certain measures
of errors (expressed in terms of primal/dual solutions and respective
approximations) while the right hand sides contain only known approximations.
Finally, we consider several examples and show that
in some simple cases these identities lead to generalized forms of the
Prager-Synge and Mikhlin’s error relations. Also, we discuss particular
cases related to power growth functionals and to the generalized Stokes
problem.
Publisher
Academy of Romanian ScientistsISSN Search the Publication Forum
2066-5997Keywords
Original source
http://www.mathematics-and-its-applications.com/preview/june2015/data/articol10.pdfPublication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/24767805
Metadata
Show full item recordCollections
Related items
Showing items with similar title or keywords.
-
A posteriori error estimates for variational problems in the theory of viscous fluids
Nokka, Marjaana (University of Jyväskylä, 2016)The papers included in the thesis are focused on functional type a posteriori error estimates for the Stokes problem, the Stokes problem with friction type boundary conditions, the Oseen problem, and the anti-plane Bingham ... -
Conditional convex orders and measurable martingale couplings
Leskelä, Lasse; Vihola, Matti (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2017)Strassen’s classical martingale coupling theorem states that two random vectors are ordered in the convex (resp. increasing convex) stochastic order if and only if they admit a martingale (resp. submartingale) coupling. By ... -
Identifying and Assessing Inter-Muscular Fat at the Distal Diaphyseal Femur Measured by Peripheral Quantitative Computed Tomography (pQCT)
Owen, Patrick J.; Hart, Nicolas H.; Latella, Christopher; Hendy, Ashlee M.; Lamon, Séverine; Rantalainen, Timo (International Society for Clinical Densitometry; Elsevier Inc., 2021)INTRODUCTION Inter/intramuscular fat can be assessed with peripheral Quantitative Computed Tomography (pQCT) and is of interest as an indicator of ‘muscle quality’. Typical pQCT scan sites (forearm, lower leg) have a low ... -
Convex analysis and dual problems
Kupiainen, Salla (2018)Tässä tutkielmassa tarkastellaan valittujen variaatiolaskennan ongelmien ja näiden duaaliongelmien välisiä suhteita. Tutkielmassa esitetään aiheen yleinen teoria ja annetaan esimerkkejä sovelluksista. -
A posteriori error bounds for approximations of the oseen problem and applications to the uzawa iteration algorithm
Nokka, Marjaana; Repin, Sergey (Walter de Gruyter GmbH, 2014)Abstract: We derive computable bounds of deviations from the exact solution of the stationary Oseen prob- lem. They are applied to approximations generated by the Uzawa iteration method. Also, we derive an ad- vanced ...