We review basic design principles underpinning the construction of the mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixedhybrid schemes, we show connections between these principles and prove that the consistency and stability conditions must lead to a member of the mimetic family of schemes regardless of the selected discretization framework. Finally, we give two examples of using flexibility of the mimetic framework: derivation of arbitraryorder schemes and inexpensive convergent schemes for nonlinear problems with small diffusion coefficients.
CITATION STYLE
Lipnikov, K., & Manzini, G. (2016). Discretization of mixed formulations of elliptic problems on polyhedral meshes. In Lecture Notes in Computational Science and Engineering (Vol. 114, pp. 309–340). Springer Verlag. https://doi.org/10.1007/978-3-319-41640-3_10
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