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

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 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. • Novel mimetic finite difference method able to deal with highly curved faces. • It achieves a convergent discrete problem which is symmetric and uses one degree of freedom for each curved face. • It can deal with geometries having curved boundaries. • It introduces a novel concept of consistency applicable to mimetic finite difference methods. [ABSTRACT FROM AUTHOR]