Algebraic error in numerical PDEs and its estimation

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Algebraic error in numerical PDEs and its estimation

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Algebraic error in numerical PDEs and its estimation

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA23-06159S" target="_blank" >GA23-06159S: Vírové struktury: pokročilé metody identifikace a efektivní numerické simulace</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Error Control, Adaptive Discretizations, and Applications, Part 1

ISBN

978-0-443-29448-8

Počet stran výsledku

51

Strana od-do

377-427

Počet stran knihy

427

Název nakladatele

Academic Press

Místo vydání

San Diego

Kód UT WoS kapitoly

001297257500009