A proof of the consistency of the finite difference technique on
Computing, 65:247-261, 2000.
also as Report SFB 256, No. 642, Univ. Bonn, 2000.
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In this paper we give a general proof of the consistency of the finite difference technique on regular sparse grids [griebel,schiekofer]. We introduce an extrapolation type discretization of differential operators on sparse grids based on the idea of the combination technique. Furthermore, we show the consistency of that discretization. Finally the equivalence of the new method with that of [griebel,schiekofer] is established.