A fractional step method on a special mesh for the resolution multidimensional evolutionary convection-diffusion problems

In this paper we consider numerical schemes for multidimensional evolutionary convection-diffusion problems, where the approximation properties are uniform in the diffusion parameter. In order to obtain an efficient 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 layers, while the fractional steps permits a low computational cost algorithm. Some numerical examples confirming the expected behavior of the method are shown.

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