Operators approximating partial derivatives at vertices of triangulations by averaging

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F10%3APU88687" target="_blank" >RIV/00216305:26110/10:PU88687 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Operators approximating partial derivatives at vertices of triangulations by averaging
Original language description
We study the problem of a high-order approximation of the partial derivatives of smooth functions u in the vertices of triangulations under the assumption that the values of u are known in the vertices of the given triangulation only. An operator A computing these approximations is said to be consistent when, for every vertex a, the approximations A(u) (a) are equal to the partial derivative of u at a for all polynomials u of degree less than or equal to two. We characterize all consistent averaging operators and show that, in general, there exists no consistent approximation of the gradient of a smooth function u by averaging.
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
<a href="/en/project/1M0579" target="_blank" >1M0579: Centre for Integrated Design of Advanced Structures</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2010
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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