The Discrete Duality Finite Volume Method for Convection-diffusion Problems

Abstract

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 cellbased gradient for the control volumes of both the primal and dual meshes, in order to achieve a higher-order accurate numerical flux for the convection term. A priori analysis is carried out to show convergence of the approximation and a global first-order convergence rate is derived. The theoretical results are confirmed by some numerical experiments.

The mimetic finite difference method for the 3D magnetostatic field problems on polyhedral meshes

“…The second step consists in reformulating the two quadrature rules (20) and (21) as a vector-matrix-vector multiplication. To this purpose, we define the m E Â m E matrix M E such that…”

“…(20) into the sum of the polyhedral contributions and apply the quadrature formula given by combining (37) and (38):…”

Study of Discrete Duality Finite Volume Schemes for the Peaceman Model

“…Therefore, we introduce the different meshes, the discrete operators and we recall the discrete duality formula. As there is a convection term in (6), we also need to define a discrete convection operator, as in [4] or [10].…”

Discrete Duality Finite Volume Method Applied to Linear Elasticity

“…Let us recall that the principle of the DDFV discretization consists in integrating the system both over a given primal mesh and a dual mesh built from the primal one. Presentation, convergence analysis and numerical tests of DDFV for diffusion, convection-diffusion and Stokes problems are available in [1], [2], [4], [8], [10], [11], [13], [14].…”