Sobolev gradient type iterative solution methods for a nonlinear 4th order elastic plate equation

Abstract

This paper considers the numerical solution of an elastic bending model of a thin plate, based on material nonlinearity, which leads to a nonlinear elliptic 4th order boundary value problem. Our goal is to summarize possible efficient iterative solvers, adapted to this problem, based on a Sobolev space background. It is proved that the proposed methods exhibit robust behaviour, that is, convergence rates are bounded independently of the considered Galerkin discretization subspace.