Algebraic error in numerical PDEs and its estimation
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F24%3A00588504" target="_blank" >RIV/67985840:_____/24:00588504 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/bs.aams.2024.04.002" target="_blank" >https://doi.org/10.1016/bs.aams.2024.04.002</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/bs.aams.2024.04.002" target="_blank" >10.1016/bs.aams.2024.04.002</a>
Alternative languages
Result language
angličtina
Original language name
Algebraic error in numerical PDEs and its estimation
Original language description
The aim of this chapter is to show that a rigorous incorporation of the algebraic error into a posteriori error analysis in numerical PDEs represents a challenging problem. An algebraic error can significantly affect both theoretical and practical estimation of the discretization error. We discuss standard residual-based error estimator and show its subtleties when generalized for estimating the total error. Then we present a derivation of the estimates based on flux reconstructions, which is from the beginning done for approximate solutions. Resulting estimates overcome the drawbacks of residual-based error estimates. In particular, we can estimate the different sources of the error, provide local error indicators, and get guaranteed bounds on the errors, which do not involve any unknown constants. On the other hand, construction of the fluxes is computationally demanding. The results are presented for the standard Poisson model problem, which is used here as a case study.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA23-06159S" target="_blank" >GA23-06159S: Vortical structures: advanced identification and efficient numerical simulation</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Error Control, Adaptive Discretizations, and Applications, Part 1
ISBN
978-0-443-29448-8
Number of pages of the result
51
Pages from-to
377-427
Number of pages of the book
427
Publisher name
Academic Press
Place of publication
San Diego
UT code for WoS chapter
001297257500009