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 faces. Crucially, it gives symmetric discrete problem uses only one unknown per face. The principle at the core of our construction is to abandon standard definition local consistency methods. Instead, we exploit novel and global concept P0-consistency. Numerical examples confirm optimal convergence rate real-case configurations having also boundaries.