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Matem. Mod., 1996, Volume 8, Number 9, Pages 25–30 (Mi mm1616)  

Proceedins of the International Conference on the Optimization of the Finite Element Approximations (OFEA-95), St.-Petersburg, 25–29 June 1995

Finite-element approximation on manifolds

Yu. K. Demjanovich

St. Petersburg State University, Department of Mathematics and Mechanics

Abstract: A method of construction of the local approximations (in particurlar – generalization of finite-element ones, for example, plane finite-elements of Courant, Zlamal, Argyris etc.) in the case of functions defined on $n$-dimensional ($n\geq1$) smooth manifold with boundary is proposed. A notion of nondegenerate simplicial subdivision of mentioned manifold is introduced, evaluations of approach and stability in Sobolev's spaces are discussed (last ones are optimal as to $N$-width of corresponding compact).

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Citation: Yu. K. Demjanovich, “Finite-element approximation on manifolds”, Matem. Mod., 8:9 (1996), 25–30

Citation in format AMSBIB
\Bibitem{Dem96}
\by Yu.~K.~Demjanovich
\paper Finite-element approximation on manifolds
\jour Matem. Mod.
\yr 1996
\vol 8
\issue 9
\pages 25--30
\mathnet{http://mi.mathnet.ru/mm1616}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1444869}
\zmath{https://zbmath.org/?q=an:0981.65510}


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