Convergence analysis of the standard central finite difference method for Poisson equation (Q292556)

The authors consider the convergence analysis of the standard central difference method for the Poisson equation. The main result is the proof of ``(...) the second-order accuracy of the numerical gradient in arbitrary smooth domains.'' (Page 604). This property of the numerical gradient is known, but has been proven only for ``simple domains''. In order to prove second-order accuracy of the numerical gradient for arbitrary domains they introduce a discrete version for the divergence theorem. Further on, they present convergence rates of their numerical tests for the Poisson problem in two and three dimensions.