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arXiv · 1610.05850

Discretization of mixed formulations of elliptic problems on polyhedral meshes

Konstantin Lipnikov·Gianmarco Manzini
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Abstract

We review basic design principles underpinning the construction of mimetic finite difference and a few finite volume and finite element schemes for mixed formulations of elliptic problems. For a class of low-order mixed-hybrid 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 higher-order schemes and convergent schemes for nonlinear problems with small diffusion coefficients.

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Konstantin Lipnikov, Gianmarco Manzini. 2016-10-19. Discretization of mixed formulations of elliptic problems on polyhedral meshes. https://arxiv.org/abs/1610.05850

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