Iterative factorization for numerical solution of elliptic equation of the fourth order in rectangular area

Abstract

The elliptic equation of the fourth order in rectangular area is considered under mixed boundary conditions. The solution is based on iterative factorization of the operator that is energetically equivalent to the operator of the solved solution. Discretization of initial task is made on the basis of method of final elements, and the precondition is selected on the basis of final differences method, thus the speed of convergence of iterative process doesn't depend on discretization parameters.