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

Abstract

We present a new mimetic finite difference method able to deal with curved faces.Notably, it yields a symmetric discrete problem which uses only one degree of freedom for each 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 convergence of the method for real-case problems with curved boundary geometries.