Article
MSC:
65N15,
65N30,
73K25,
74B99,
74H99,
74P99,
74S05 | MR 0640139 | Zbl 0488.73072 | DOI: 10.21136/AM.1982.103944
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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
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
Summary:
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.
References:
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