Matrix approach to mimetic discretizations for differential operators on non-uniform grids

Recent investigations have led to a method based on matrix analysis for the construction of high order discrete, fourth and higher mimetic operators, divergence and gradient. These operators have the same order of accuracy in the interior as well as at the boundary on uniform grids. This paper extends the method to non-uniform staggered grids. Here we present this extension on second-order operators although the method works for any order of accuracy. In addition, the boundary operator that allows the operators to satisfy a discrete analog of the divergence theorem is constructed.