Convergence rate of a finite volume scheme for the linear convection-diffusion equation on locally refined meshes
Mathématiques pour l'Industrie et la Physique, UMR 5640, INSA,
135 avenue de Rangueil, 31077 Toulouse Cedex 4, France. (Yves.Coudiere@sophia.inria.fr)
2 ONERA, Centre de Toulouse, 2 avenue Ed. Belin, 31055 Toulouse Cedex 4, France. (Philippe.Villedieu@cert.fr)
Revised: 28 June 2000
We study a finite volume method, used to approximate the solution of the linear two dimensional convection diffusion equation, with mixed Dirichlet and Neumann boundary conditions, on Cartesian meshes refined by an automatic technique (which leads to meshes with hanging nodes). We propose an analysis through a discrete variational approach, in a discrete H1 finite volume space. We actually prove the convergence of the scheme in a discrete H1 norm, with an error estimate of order O(h) (on meshes of size h).
Mathematics Subject Classification: 65C20 / 65N12 / 65N15 / 76R50 / 45L10
Key words: Finite volumes / mesh refinement / convection-diffusion / convergence rate.
© EDP Sciences, SMAI, 2000