On the problem of combination of finite-difference and finite-element schemes in gas-dynamic problems with thermal conductivity

Schemes with thermodynamic functions of density, temperature, pressure defined in centers of tetragonal cells are considered for gas dynamic equations (center schemes). Schemes with temperature defined in nodes-tops of tetragon are considered for the thermal conductivity equation (node schemes, in particular, finite-element ones).
Need appears of double interpolations of temperatures from nodes to centers and vice versa for combining of node and center schemes. This leads to the schemes with conditional approximation. Method of transformation of node schemes to interpolation-invariant ones ($I$-schemes) is offered in the report, $I$-scheme – is a scheme, which stays unchangeable under double interpolations of net temperature.