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.
Reviewer: C.I.Gheorghiu (Cluj-Napoca)
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 |