On a residual-based a posteriori error estimator for the total error
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384843" target="_blank" >RIV/00216208:11320/18:10384843 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1093/imanum/drx037" target="_blank" >https://doi.org/10.1093/imanum/drx037</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1093/imanum/drx037" target="_blank" >10.1093/imanum/drx037</a>
Alternative languages
Result language
angličtina
Original language name
On a residual-based a posteriori error estimator for the total error
Original language description
A posteriori error analysis in numerical partial differential equations aims at providing sufficiently accurate information about the distance of the numerically computed approximation to the true solution. Besides estimating the total error, a posteriori analysis should also provide information about its discretization and (inexact) algebraic computation parts. This issue has been addressed by many authors using different approaches. Historically, probably the first and practically very important approach is based on combination of the classical residual-based bound on the discretization error with the adaptive hierarchy of discretizations and computations that allow to incorporate, using various heuristic arguments, the algebraic error. Motivated by some recent publications, this text uses a complementary approach and examines subtleties of the (generalized) residual-based a posteriori error estimator for the total error that rigorously accounts for the algebraic part of the error. The aim is to show on the standard Poisson model problem example, which is used here as a case study, that a rigorous incorporation of the algebraic error represents an intriguing problem that is not yet completely resolved. That should be of concern in h-adaptivity approaches, where the refinement of the mesh is determined using the residual-based a posteriori error estimator assuming Galerkin orthogonality. The commonly used terminology such as 'guaranteed computable upper bounds' should be in the presence of algebraic error cautiously examined.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/LL1202" target="_blank" >LL1202: Implicitly constituted material models: from theory through model reduction to efficient numerical methods</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
IMA Journal of Numerical Analysis
ISSN
0272-4979
e-ISSN
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Volume of the periodical
38
Issue of the periodical within the volume
3
Country of publishing house
GB - UNITED KINGDOM
Number of pages
21
Pages from-to
1164-1184
UT code for WoS article
000450010000003
EID of the result in the Scopus database
2-s2.0-85057148101