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Convergence rate of a finite volume scheme for a two dimensional convection-diffusion problem. (English) Zbl 0937.65116
The authors propose a class of cell centered finite volume schemes on general unstructured meshes in order to solve a linear convection-diffusion problem. An upwind scheme and the so-called diamond cell method are used, respectively, to treat the convective and diffusive terms. An error estimate of order $$h$$ on a mesh of quadrangles is the main result of the paper.

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations
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