Iterative solution of some schemes of the finite element method for elliptic equations of order $2n$, $n\ge1$

Five-point (in the two-dimehsional case) mesh operators A are constructed, equivalent in spectrum to mesh operators of schemes of the finite element method, for solving elliptic equations of order $2n$, $n\ge1$. An efficient direct method is also developed for solving systems of algebraic equations $Au=f$ with an estimate $O(h^{-2}\ln h^{-1})$ of the number of arithmetic operations, where $h$ is the mesh parameter.