An equilibrium finite element method in three-dimensional elasticity

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.