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Center for Nonlinear Studies |
We present a new Mimetic Finite Difference method for the diffusion problem that is based on a linear interpolation for the numerical fluxes. The scalar solution field is approximated by a piecewise constant function. This approach provides a second-order accurate approximation to the flux of the exact solution. In analogy with the original formulation, a family of local scalar products is constructed to satisfy the fundamental properties of local consistency and spectral stability. Optimal convergence rates and accuracy improvement with respect to the lower-order formulation are shown by numerical examples.
Host: Mikhail Shashkov