Estimate of the convergence rate of a difference scheme for an elliptic operator of the fourth order in a domain of arbitrary form (Q2703303)

The author proposes a difference scheme for the solution of the Dirichlet problem: \(\Delta^2 u-\sum_{i=1}^{2}{\partial\over\partial x_{i}} (K_{i}(x){\partial u\over\partial x_{i}})+q(x)u=f(x)\), \(x\in\Omega\); \(u(x)={\partial u(x)\over\partial n}=0, x\in\partial\Omega\), where \(n\) is the external normal to \(\partial \Omega\), \(f(x)\in L_{2}(\Omega)\), \(q(x)\in L_{\infty}(\Omega), q(x)\geq 0\). The method of fictitious domains is used and the order of accuracy of the proposed difference scheme is established.