The Discrete Duality Finite Volume Method for Convection-diffusion Problems

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. Key words. convection-diffusion equation, discrete duality finite volume method, polynomial reconstruction, diamond scheme, unstructured meshes, polygonal meshes AMS subject classifications. 35J05, 35J25, 65N12, 65N15, 65N30 DOI. 10.1137/080731219

• Type: Journal
• Year: 2010
• Where: SIAMNUM
• Authors: Yves Coudière, Gianmarco Manzini
• Keywords: Discrete Duality Finite, Duality Finite Volume, Polygonal Meshes Ams, SIAMNUM 2010