Mimetic finite difference operators for second-order tensors on unstructured grids

We use the support operators method to derive discrete approximations for the gradient of a vector and divergence of a tensor on unstructured grids in two dimensions. These discrete operators satisfy discrete analogs of the integral identities of the differential operators on unstructured grids where vector functions are defined at the grid points, and tensor functions are defined as tangential projections to the zone edges, or as normal projections to the median mesh. We evaluate the accuracy of the discrete operators by determining the order of convergence of the truncation error on structured and unstructured grids, and show that the truncation error of the method is between first and second order depending on the smoothness of the grid. In a test problem on a highly nonuniform grid, we confirm that the convergence rate is between first and second order.