A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F13%3A10159214" target="_blank" >RIV/00216208:11320/13:10159214 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/110859282" target="_blank" >http://dx.doi.org/10.1137/110859282</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/110859282" target="_blank" >10.1137/110859282</a>
Alternative languages
Result language
angličtina
Original language name
A FRAMEWORK FOR ROBUST A POSTERIORI ERROR CONTROL IN UNSTEADY NONLINEAR ADVECTION-DIFFUSION PROBLEMS
Original language 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 t
Czech name
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Czech description
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Classification
Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/GA201%2F08%2F0012" target="_blank" >GA201/08/0012: Qualitative analysis and numerical solution of flow problems</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
SIAM Journal on Numerical Analysis
ISSN
0036-1429
e-ISSN
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Volume of the periodical
51
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
773-793
UT code for WoS article
000318405100002
EID of the result in the Scopus database
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