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The numerical solution of partial differential equations with finite differencesmimetic methods that satisfy properties of the continuumdifferential operators and mimic discrete versions of appropriate integral identities  is more likely to produce better approximations. Recently, one of the authors  developed a systematic approach to obtain mimetic finite difference discretizations for divergence   and gradient operators, which achieves the same order of accuracy on the boundary and inner grid    points. This paper uses the second-order version of those operators to develop a new mimetic finite    difference method for the steady-state diffusion equation. A complete theoretical and numerical    analysis of this new method is presented, including an original and nonstandard proof of the quadratic    convergence rate of this new method. The numerical results agree in all cases with our theoreticalanalysis, providing strong evidence that the new method is a better choice than the standard finitedifference method

Convergence of a Mimetic Finite Difference Method for Static Diffusion Equation