Numerical Solution of Elliptic Convection - Di usionProblems on Fitted

The problem of the transport of a quantity (heat, matter or momentum) by advection-diiusion is considered for arbitrarily large Peclet number in a two-dimensional domain. In some neighbourhoods of the boundary of the domain, boundary layers may appear for large Peclet number. It is well known that classical nite diierence methods do not yield approximate solutions with a guaranteed accuracy if the Peclet number can be arbitrarily large. For such problems, numerical methods which use monotone nite diierence operators on appropriately tted piecewise-uniform meshes have been shown to yield approximate solutions with a guaranteed accuracy independent of the Peclet number. Numerical examples are presented which verify this property under various boundary conditions, and comparisons are made with approximate solutions obtained using alternatively tted meshes.