On the supraconvergence of elliptic finite difference schemes (Q1294518)

The paper deals with supraconvergence of a finite difference scheme for second-order elliptic boundary value problems \[ -(au_x)_x- (bu_x)_y- (bu_y)_x- (cu_y)_y+ du_x+ eu_y+ fu= g\quad\text{in }\Omega\subset R^2, \] subject to Dirichlet boundary conditions in polynomial regions. The authors prove supraconvergence of the considered finite difference scheme. Their approach allows consideration of problems with variable coefficients, mixed derivatives and polygonal domains. The authors develop close relations between the supraconvergence of a finite difference scheme and a certain finite element method.