We present a new mimetic finite difference method for diffusion problems that converges on grids with 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 P0-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.

The curved mimetic finite difference method: Allowing grids with curved faces / Pitassi, Silvano; Ghiloni, Riccardo; Petretti, Igor; Trevisan, Francesco; Specogna, Ruben. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - STAMPA. - 490:(2023), pp. 11229401-11229418. [10.1016/j.jcp.2023.112294]

The curved mimetic finite difference method: Allowing grids with curved faces

Pitassi, Silvano;Ghiloni, Riccardo;Specogna, Ruben
2023-01-01

Abstract

We present a new mimetic finite difference method for diffusion problems that converges on grids with 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 P0-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.
2023
Pitassi, Silvano; Ghiloni, Riccardo; Petretti, Igor; Trevisan, Francesco; Specogna, Ruben
The curved mimetic finite difference method: Allowing grids with curved faces / Pitassi, Silvano; Ghiloni, Riccardo; Petretti, Igor; Trevisan, Francesco; Specogna, Ruben. - In: JOURNAL OF COMPUTATIONAL PHYSICS. - ISSN 0021-9991. - STAMPA. - 490:(2023), pp. 11229401-11229418. [10.1016/j.jcp.2023.112294]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/410432
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