Estimates of the rate of convergence of difference schemes for fourth-order elliptic equations

The second boundary value problem is considered for two-dimensional linear and quasilinear fourth-order elliptic equations in a rectangle, when the solution belongs to classes $W^{3+s}_2(\Omega)$, $s=0,1$. Using operators of exact difference schemes, schemes are constructed for which convergence-rate estimates of order $O(|h|^{1+s})$ in the mesh norm of $W^2_2(\omega)$ are established.