The time filter for the non-stationary coupled Stokes/Darcy model

In this paper, we consider the effect of adding a simple time filter to the Backward Euler scheme for the non-stationary coupled Stokes/Darcy model. The method is modular and requires only one additional line of code to be added, which improves the accuracy of the Backward Euler scheme from first to second order. We verify this conclusion from both theoretical analysis and numerical experiments. Finally, we propose that the BDF2 scheme can be improved to the third order if the time filter is added, which is demonstrated by numerical experiments. (C) 2019 IMACS. Published by Elsevier B.V. All rights reserved.