A FRACTIONAL STEP METHOD ON A SPECIAL MESH FOR THE RESOLUTION OF MULTIDIMENSIONAL EVOLUTIONARY CONVECTION-DIFFUSION PROBLEMS

In this paper we consider numerical schemes for multidimensional evolu tionary convection-diffusion problems, where the approximation propert ies are uniform in the diffusion parameter. In order to obtain an effi cient method, to provide good approximations with independence of the size of the diffusion parameter, we have developed a numerical method which combines a finite difference spatial discretization on a special mesh and a fractional step method for the time variable. The special mesh allows a correct approximation of the solution in the boundary la yers, while the fractional steps permits a law computational cost algo rithm. Some numerical examples confirming the expected behavior of the method are shown, (C) 1998 Elsevier Science B.V. and IMACS. All right s reserved.