On the rate of convergence for approximation of an eigenvalue problem describing vibrations of axisymmetric revolution elastic shells

In this paper, we provide the rate of convergence for approximation of an eigenvalue problem describing vibrations of axisymmetric revolution elastic shells. The eigenvalue problem approximation is constructed by the method of finite elements. We study a system of differential equations with variable coefficients, some of which are non-integrable improperly near 0. To this aim, certain special weighted spaces are used, which were introduced earlier by the author.