Distribution of the discretization and algebraic error in numerical solution of partial differential equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F14%3A10286559" target="_blank" >RIV/00216208:11320/14:10286559 - isvavai.cz</a>
Alternative codes found
RIV/67985807:_____/14:00428023
Result on the web
<a href="http://dx.doi.org/10.1016/j.laa.2014.02.009" target="_blank" >http://dx.doi.org/10.1016/j.laa.2014.02.009</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.laa.2014.02.009" target="_blank" >10.1016/j.laa.2014.02.009</a>

Result language
angličtina
Original language name
Distribution of the discretization and algebraic error in numerical solution of partial differential equations
Original language description
In the adaptive numerical solution of partial differential equations, local mesh refinement is used together with a posteriori error analysis in order to equilibrate the discretization error distribution over the domain. Since the discretized algebraic problems are not solved exactly, a natural question is whether the spatial distribution of the algebraic error is analogous to the spatial distribution of the discretization error. The main goal of this paper is to illustrate using standard boundary valuemodel problems that this may not hold. On the contrary, the algebraic error can have large local components which can significantly dominate the total error in some parts of the domain. The illustrated phenomenon is of general significance and it is notrestricted to some particular problems or dimensions. To our knowledge, the discrepancy between the spatial distribution of the discretization and algebraic errors has not been studied in detail elsewhere.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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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>S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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