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
Päivämäärä
2015Tekijänoikeudet
© 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.
Julkaisija
Academy of Romanian ScientistsISSN Hae Julkaisufoorumista
2066-5997Asiasanat
Alkuperäislähde
http://www.mathematics-and-its-applications.com/preview/june2015/data/articol10.pdfJulkaisu tutkimustietojärjestelmässä
https://converis.jyu.fi/converis/portal/detail/Publication/24767805
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