Incremental unknowns method based on the theta-scheme for time-dependent convection-diffusion equations
A theta-scheme using two-level incremental unknowns is presented for solving time-dependent convection-diffusion equations in two-dimensional case. The IMG algorithm (Inertial Manifold-Multigrid algorithm) including the second-order incremental unknowns is convergent. The incremental unknowns method based on the theta-scheme needs a stability condition as 0 <= theta <= 1/2 and is unconditionally stable as 1/2 <= theta <= 1. By the GMRES method in the iteration at each time step, numerical results of the convection-diffusion equations are investigated and confirm that oscillations can be controlled by the incremental unknowns method. (C) 2008 IMACS. Published by Elsevier B.V. All rights reserved.
incremental unknowns theta-scheme convection-diffusion equation