A Proof of the Consistency of the Finite Difference Technique on Sparse Grids

In this paper, we give a proof of the consistency of the finite difference technique on regular sparse grids 7, 18]. We introduce an extrapolation-type discretization of differential operators on sparse grids based on the idea of the combination technique and we show the consistency of this discretization. The equivalence of the new method with that of 7, 18] is established. Received February 8, 2000; revised June 8, 2000