In the present paper the application of the residual-free bubbles (RFB) method to eigenvalue problems is considered. Problems for the elliptic operator in one- and two-dimensional domains are considered. The proof that the RFB method is equivalent to the of finite elements method with special basic functions is presented, i.e. it is possible to choose basic functions in the finite elements method in such a manner that the same discrete problem appears, as in the RFB method. Methods of the solution of nonlinear matrix eigenvalue problems, which appear as a result of the RFB method application to eigenvalue problems are considered.

Mathematical problems and theory of numerical methods