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arXiv · 2203.13105

The curved Mimetic Finite Difference method: allowing grids with curved faces

Silvano Pitassi·Riccardo Ghiloni·Igor Petretti·Francesco Trevisan·Ruben Specogna
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Abstract

We present a new mimetic finite difference method for diffusion problems that converges on grids with \textit{curved} (i.e., non-planar) faces. Crucially, it gives a symmetric discrete problem that uses only one discrete unknown per curved face. The principle at the core of our construction is to abandon the standard definition of local consistency of mimetic finite difference methods. Instead, we exploit the novel and global concept of $P_{0}$-consistency. Numerical examples confirm the consistency and the optimal convergence rate of the proposed mimetic method for cubic grids with randomly perturbed nodes as well as grids with curved boundaries.

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Silvano Pitassi, Riccardo Ghiloni, Igor Petretti, Francesco Trevisan, Ruben Specogna. 2022-03-24. The curved Mimetic Finite Difference method: allowing grids with curved faces. https://doi.org/10.1016/j.jcp.2023.112294

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