A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F10%3A00342835" target="_blank" >RIV/67985807:_____/10:00342835 - isvavai.cz</a>
Alternative codes found
RIV/46747885:24220/10:#0001647
Result on the web
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DOI - Digital Object Identifier
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Alternative languages
Result language
angličtina
Original language name
A Posteriori Error Estimates Including Algebraic Error and Stopping Criteria for Iterative Solvers
Original language description
For the finite volume discretization of a second-order elliptic model problem, we derive a posteriori error estimates which take into account an inexact solution of the associated linear algebraic system. We show that the algebraic error can be bounded by constructing an equilibrated Raviart-Thomas-Nédélec discrete vector field whose divergence is given by a proper weighting of the residual vector. Next, claiming that the discretization error and the algebraic one should be in balance, we construct stopping criteria for iterative algebraic solvers.Using this convenient balance, we also prove the efficiency of our a posteriori estimates; i.e., we show that they also represent a lower bound, up to a generic constant, for the overall energy error. A localversion of this result is also stated. This makes our approach suitable for adaptive mesh refinement which also takes into account the algebraic error.
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
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)
Others
Publication year
2010
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 Scientific Computing
ISSN
1064-8275
e-ISSN
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Volume of the periodical
32
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
24
Pages from-to
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UT code for WoS article
000278576300022
EID of the result in the Scopus database
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