High-Order Mimetic Finite Difference Methods on Nonuniform Grids

By combining the support-operators method with the mapping method, we have derived new mimetic fourthorder accurate discretizations of the divergence, gradient, and Laplacian on nonuniform grids. These finite difference operators mimic the differential and integral identities satisfied by the differential operators. For example, the discrete divergence is the negative of the adjoint of the discrete gradient and consequently the Laplacian is a symmetric negative operator. •Ve analyze the loss of accuracy in the approximations when the grid is rough and include numerical examples demonstrating the effectiveness of the higher order methods on nonuniform grids in one and two dimensions. The analysis and examples are for fourthorder finite difference methods, but the approach can be extended to create approximations of arbitrarily high order.

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