The Discrete Duality Finite Volume Method for Convection Diffusion Problems

Yves Coudière (1) , Gianmarco Manzini (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IMATI-CNR - Istituto di Matematica Applicata e Tecnologie Informatiche

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 how convergence of the approximation and a global first-order convergence rate is derived. The theoretical results are confirmed bysome numerical experiments.

Mots clés: polygonal meshes.; Convection-dffusion equation; discrete duality finite volume method; polynomial reconstruction; diamond scheme; unstructured meshes; polygonal meshes

Domaines: Analyse numérique [math.NA]

Yves Coudière, Gianmarco Manzini. The Discrete Duality Finite Volume Method for Convection Diffusion Problems. SIAM Journal on Numerical Analysis, 2010, 47 (6), pp.4163-4192. ⟨hal-00319254⟩