An analysis of viscous splitting and adaptivity for steady-state convection-diffusion problems (Q1090207)

This paper analyzes a viscous splitting approach for the solution of steady-state convection-diffusion problems with constant coefficients. The main advantage of this approach is that the convective and diffusive parts of the equation can be treated separately. A Fourier analysis is provided for both the fully discrete problem in one space dimension and the semi-discrete problem in N space dimensions. Nearly optimal solutions and meshes were generated using an adaptive mesh refinement strategy for a model one-dimensional problem.