Construction of economic discrete models in problems of plate theory (Q403940)

This article completes the series of the author's works on the construction of economic numerical methods for the solving of the following problems in plate theory: to find a function \(u\), satisfying the biharmonic equation \[ \triangle^2 u=f \qquad x_1,x_2 \in \Omega \subset \mathbb{R}^2 \] with one of the following boundary conditions on the boundary \(\gamma=\partial\Omega\) (1) \(u|_{\gamma}=0, \; \frac{du}{dn}|_{\gamma}=0\) (damped); (2) \(\left(\frac{\partial^2 u}{\partial x_1^2}+\nu\frac{\partial^2 u}{\partial x_2^2}\right)|_{\gamma}=0,\;\left(\frac{\partial^3 u}{\partial x_1^3}+(2-\nu)\frac{\partial^3 u}{\partial x_1\partial x_2^2}\right)|_{\gamma}=0\) (free support); (3) \(u|_{\gamma}=0, \; \triangle u|_{\gamma}=0\) (hinged support).