High-order mimetic finite-difference operators satisfying the extended Gauss divergence theorem

Abstract

We present high-order mimetic finite-difference operators that satisfy the extended Gauss theorem. These operators have the same order of accuracy in the interior and at the boundary, no free parameters and optimal bandwidth. They are defined over staggered grids, using weighted inner products with a diagonal norm. We present several examples to demonstrate that mimetic finite-difference schemes using these operators produce excellent results.