About diagonalization of matrixes in a method of final elements at the non-stationary boundary problems

The point of view of the author on some priority questions in the field of development and application of final element method is stated. The algorithm of application of final element method with diagonalized matrixes of resolving systems of the linear algebraic equations in problems of heat convection of liquid is stated. It is given an example algorithm applications for the solution of a technical problem of receiving high-quality steel body by a method of mathematical modeling.