INCREMENTAL UNKNOWNS ON NONUNIFORM MESHES

This article is devoted to the numerical analysis of the Incremental U nknowns method (IU) when applied to nonuniform meshes. The extension o f the IU we propose here is devoted to the numerical solution of bound ary value problems e.g. in the presence of boundary layers which neces sitate the use of refined grids near the boundary We define the increm ental unknowns in this context and we introduce the corresponding hier archical preconditioners in space dimensions one and two for the Poiss on problem. We establish the coercivity of the linens operator using t he incremental unknowns. We also obtain numerical results on the asymp totic behaviour of the condition number of the underlying matrices tha t are comparable to the ones derived in the uniform case in space dime nsion one. In space dimension two we do not recover the same asymptoti c results but the condition number is considerably reduced with our pr econditioner. The numerical examples we give concern the solution of e lliptic problems on particular meshes used for boundary layer problems in Computational Fluid Dynamics. Futhermore, we construct high order IUs in the nonuniform case by a generalization of the interpolation co mpact schemes. (C) Elsevier; Paris.