This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical
and physical systems including conservation laws, symmetry and positivity of solutions …

A symmetric discretization scheme for heterogeneous anisotropic diffusion problems on
general meshes is developed and studied. The unknowns of this scheme are the values at …

We analyze the joint efforts made by the geometry processing and the numerical analysis
communities in the last decades to define and measure the concept of “mesh quality” …

We present a finite volume method for the numerical approximation of advection–diffusion
problems in convection-dominated regimes. The method works on unstructured grids formed …

In this paper, a nonlinear positivity-preserving finite volume scheme for the heterogeneous
and anisotropic diffusion problems is proposed. Firstly, a linear diamond finite volume …

A finite volume method is presented for discretizing 3D diffusion operators with variable full
tensor coefficients. This method handles anisotropic, non-symmetric or discontinuous …

We present in this article a positive finite volume method for diffusion equation on deformed
meshes. This method is mainly inspired from, and uses auxiliary unknowns at the nodes of …

We present a post-processing technique for the mimetic finite difference solution of diffusion
problems in mixed form. Our post-processing method yields a piecewise linear …

In this paper we extend the discrete duality finite volume (DDFV) formulation to the steady
convection-diffusion equation. The discrete gradients defined in DDFV are used to define a …