Geodesic
Curved triangular finite $C^m$-elements
Applications of Mathematics, Tome 23 (1978) no. 5, pp. 346-377

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Curved triangular $C^m$-elements which can be pieced together with the generalized Bell's $C^m$-elements are constructed. They are applied to solving the Dirichlet problem of an elliptic equation of the order $2(m+1)$ in a domain with a smooth boundary by the finite element method. The effect of numerical integration is studied, sufficient conditions for the existence and uniqueness of the approximate solution are presented and the rate of convergence is estimated. The rate of convergence is the same as in the case of polygonal domains when the generalized Bell's $C^m$-elements are used.
DOI : 10.21136/AM.1978.103761
Classification : 35A35, 35J40, 65M99, 65N30, 65N99
Keywords: generalized Bell’s $C^m$-elements; approximate solution; rate of convergence 
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     title = {Curved triangular finite $C^m$-elements},
     journal = {Applications of Mathematics},
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Ženíšek, Alexander. Curved triangular finite $C^m$-elements. Applications of Mathematics, Tome 23 (1978) no. 5, pp. 346-377. doi: 10.21136/AM.1978.103761

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