The Discrete Duality Finite Volume Method for Convection-diffusion Problems

Authors:
Yves Coudière;Gianmarco Manzini
Affiliations:
Yves.Coudiere@math.univ-nantes.fr;Marco.Manzini@imati.cnr.it
Venue:
SIAM Journal on Numerical Analysis
Year:
2010

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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 cell-based 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.