Numerical schemes of the support operators method for elasticity theory equations

In this paper there are considered steady-state equations of linear elasticity theory, for which a family of difference schemes based on support-operators method is constructed. The scalar product in the space of tensor mesh functions, strain tensor component, is selected according to the energy of deformed body. On the unstructured grids there are constructed and analyzed invariant to rotations difference schemes based on support-operators method for the elasticity theory equations in the shifts. The convergence of these schemes to the first order in the mean-square sense for the symmetrized displacement tensor components is proved.