Incremental unknowns method based on the theta-scheme for time-dependent convection-diffusion equations

  title={Incremental unknowns method based on the theta-scheme for time-dependent convection-diffusion equations},
  author={Lunji Song and Yujiang Wu},
  journal={Math. Comput. Simul.},
A θ-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 θ-scheme needs a stability condition as 0 ≤ θ < 1/2 and is unconditionally stable as 1/2 ≤ θ ≤ 1. By the GMRES method in the iteration at each time step, numerical results of the convection… Expand
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