CONVERGENCE RATE OF A FINITE VOLUME SCHEME FOR A TWO DIMENSIONAL CONVECTION-DIFFUSION PROBLEM

In this paper, a class of cell centered nite volume schemes, on general unstructured meshes, for a linear convection-diusion problem, is studied. The convection and the diusion are respectively approximated by means of an upwind scheme and the so called diamond cell method (4). Our main result is an error estimate of order h, assuming only the W 2;p (for p> 2) regularity of the continuous solution, on a mesh of quadrangles. The proof is based on an extension of the ideas developed in (12). Some new diculties arise here, due to the weak regularity of the solution, and the necessity to approximate the entire gradient, and not only its normal component, as in (12).

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