Estimating and localizing the algebraic and total numerical errors using flux reconstructions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10384848" target="_blank" >RIV/00216208:11320/18:10384848 - isvavai.cz</a>

Alternative codes found

RIV/67985807:_____/18:00481663

Result on the web

<a href="https://doi.org/10.1007/s00211-017-0915-5" target="_blank" >https://doi.org/10.1007/s00211-017-0915-5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00211-017-0915-5" target="_blank" >10.1007/s00211-017-0915-5</a>

Result language

angličtina

Original language name

Estimating and localizing the algebraic and total numerical errors using flux reconstructions

Original language description

This paper presents a methodology for computing upper and lower bounds for both the algebraic and total errors in the context of the conforming finite element discretization of the Poisson model problem and an arbitrary iterative algebraic solver. The derived bounds do not contain any unspecified constants and allow estimating the local distribution of both errors over the computational domain. Combining these bounds, we also obtain guaranteed upper and lower bounds on the discretization error. This allows to propose novel mathematically justified stopping criteria for iterative algebraic solvers ensuring that the algebraic error will lie below the discretization one. Our upper algebraic and total error bounds are based on locally reconstructed fluxes in , whereas the lower algebraic and total error bounds rely on locally constructed -liftings of the algebraic and total residuals. We prove global and local efficiency of the upper bound on the total error and its robustness with respect to the approximation polynomial degree. Relationships to the previously published estimates on the algebraic error are discussed. Theoretical results are illustrated on numerical experiments for higher-order finite element approximations and the preconditioned conjugate gradient method. They in particular witness that the proposed methodology yields a tight estimate on the local distribution of the algebraic and total errors over the computational domain and illustrate the associated cost.

Czech name

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Czech description

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Type

J_imp - 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

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>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2018

Confidentiality

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

Name of the periodical

Numerische Mathematik

ISSN

0029-599X

e-ISSN

—

Volume of the periodical

138

Issue of the periodical within the volume

3

Country of publishing house

DE - GERMANY

Number of pages

41

Pages from-to

681-721

UT code for WoS article

000426063200006

EID of the result in the Scopus database

2-s2.0-85028846639