Geodesic
An equilibrium finite element method in three-dimensional elasticity
Applications of Mathematics, Tome 27 (1982) no. 1, pp. 46-75.

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The tetrahedral stress element is introduced and two different types of a finite piecewise linear approximation of the dual elasticity problem are investigated on a polyhedral domain. Fot both types a priori error estimates $O(h^2)$ in $L_2$-norm and $O(h^{1/2})$ in $L_\infty$-norm are established, provided the solution is smooth enough. These estimates are based on the fact that for any polyhedron there exists a strongly regular family of decomprositions into tetrahedra, which is proved in the paper, too.
DOI : 10.21136/AM.1982.103944
Classification : 65N15, 65N30, 73K25, 74B99, 74H99, 74P99, 74S05
Keywords: composite tetrahedral equilibrium element; two types of finite approximation; three-dimensional problem; polyhedral domain; Castigliano-Menabrea’s principle; minimum complementary energy; a priori error estimates; existence of strongly regular family of decompositions 
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     title = {An equilibrium finite element method in three-dimensional elasticity},
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Křížek, Michal. An equilibrium finite element method in three-dimensional elasticity. Applications of Mathematics, Tome 27 (1982) no. 1, pp. 46-75. doi : 10.21136/AM.1982.103944. http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103944/

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