where aik = a k i are C ~ functions. We shall be concerned with the solution of this problem by certain finite difference schemes described in Bramble, Kellogg, and Thom6e E2] and in particular with the convergence properties of these schemes near plane portions of B. Let h be a (small) positive parameter and consider the set E~ of mesh-points x = (n lh . . . . . n N h), n i integers. We say that the mesh-point x is all interior mesh-point of R, or x c R h if {y; [ y i x i [ <=h, j = t . . . . . N}CR. The remaining mesh-points in R form the set B h of boundary mesh-points. Let e i be the j-th unit vector. For real mesh-functions we define the forward, backward, and symmetric difference quotient operators,