Geodesic
Finite-element approximation on manifolds
Matematičeskoe modelirovanie, Tome 8 (1996) no. 9, pp. 25-30.

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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). 
@article{MM_1996_8_9_a2,
     author = {Yu. K. Demjanovich},
     title = {Finite-element approximation on manifolds},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {25--30},
     publisher = {mathdoc},
     volume = {8},
     number = {9},
     year = {1996},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MM_1996_8_9_a2/}
}
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Yu. K. Demjanovich. Finite-element approximation on manifolds. Matematičeskoe modelirovanie, Tome 8 (1996) no. 9, pp. 25-30. http://geodesic.mathdoc.fr/item/MM_1996_8_9_a2/