On Efficient Numerical Solution of Linear Algebraic Systems Arising in Goal-Oriented Error Estimates
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F20%3A10419200" target="_blank" >RIV/00216208:11320/20:10419200 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=y53rf3rVyf" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=y53rf3rVyf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10915-020-01188-y" target="_blank" >10.1007/s10915-020-01188-y</a>
Alternative languages
Result language
angličtina
Original language name
On Efficient Numerical Solution of Linear Algebraic Systems Arising in Goal-Oriented Error Estimates
Original language description
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The goal-oriented error estimates require the solution of the primal as well as dual algebraic systems. We solve both systems simultaneously using the bi-conjugate gradient method which allows to control the algebraic errors of both systems. We develop a stopping criterion which is cheap to evaluate and guarantees that the estimation of the algebraic error is smaller than the estimation of the discretization error. Using this criterion and an adaptive mesh refinement technique, we obtain an efficient and robust method for the numerical solution of PDEs, which is demonstrated by several numerical experiments.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics
Result continuities
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)
Others
Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Scientific Computing
ISSN
0885-7474
e-ISSN
—
Volume of the periodical
83
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
29
Pages from-to
5
UT code for WoS article
000522128600002
EID of the result in the Scopus database
2-s2.0-85082059857