A Defect Correction Method for the Evolutionary Convection - Diffusion Problem with Increased Time Accuracy

This work extends the results of [L07] by presenting a defect correction method with increased time accuracy. The desired time accuracy is attained with no extra computational cost. The method is applied to the evolutionary transport problem, and is proven to be unconditionally stable. In the defect step, the artificial viscosity parameter is added to the Peclet number as a stability factor, and the system is antidiffused in the correction step. The time accuracy is also increased in the correction step by modifying the right hand side. Hence, we solve the transport problem twice, using the Crank-Nicolson scheme (with the artificial viscosity parameter added), and obtain the accuracy of O(h2 +k4). The computational results are provided, that verify the claimed space and time accuracy of the approximate solution.