What is the smallest possible constatnt in Céa´s lemma?

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F06%3A00041049" target="_blank" >RIV/67985840:_____/06:00041049 - 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
What is the smallest possible constatnt in Céa´s lemma?
Original language description
We consider finite element approximations of a second order elliptic problem on a bounded polytopic domain in Rd with d in {1,2,3,...}. The constatnt C> 1 appearing in Céa´s lemma and coming from its standard proof can be very large when the coefficientsof an elliptic operator attain considerably different values. We restrict ourselves to regular families of uniform partitions and linear simplicial elements. Using a lower bound of the interpolation error and the supercloseness between the finite element solution and the Lagrange interpolant of the exact solution, we show that the ratio between discretization and interpolation errors is equal to 1 + 0(h) as the discretization parameter h tends to zero. Numerical results in one and two-dimensional caseillustrating this phenomenon are presented.
Czech name
Jaká je nejmenší konstanta v Céově lemmatu?
Czech description
Pomocí teorie superkonvergence je ukázáno, že minimální možná konstanta v Céově lemmatu je velice blízko 1.

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/IAA1019201" target="_blank" >IAA1019201: The finite element method for three-dimensional problems</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2006
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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