Defect-correction finite element method based on Crank-Nicolson extrapolation scheme for the transient conduction-convection problem with high Reynolds number

A defect-correction finite element (FE) method is designed and analyzed for solving the two-dimensional (2D) transient conduction-convection problem at high Reynolds number. The method combines the merits of Crank-Nicolson (CN) extrapolation discretization and defect-correction scheme, which consists of solving a linearized problem with an added artificial viscosity term and then correcting the previous numerical solutions by a linearized defect-correction technique. The stability and optimal error estimate of the fully discrete scheme are derived. Finally, performance of the proposed method is investigated by numerical experiments.