On a residual-based a posteriori error estimator for the total error

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

On a residual-based a posteriori error estimator for the total error

Popis výsledku v původním jazyce

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 &apos;guaranteed computable upper bounds&apos; should be in the presence of algebraic error cautiously examined.

Název v anglickém jazyce

On a residual-based a posteriori error estimator for the total error

Popis výsledku anglicky

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 &apos;guaranteed computable upper bounds&apos; should be in the presence of algebraic error cautiously examined.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/LL1202" target="_blank" >LL1202: Materiály s implicitními konstitutivními vztahy: Od teorie přes redukci modelů k efektivním numerickým metodám</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

IMA Journal of Numerical Analysis

ISSN

0272-4979

e-ISSN

—

Svazek periodika

38

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

21

Strana od-do

1164-1184

Kód UT WoS článku

000450010000003

EID výsledku v databázi Scopus

2-s2.0-85057148101