Adaptive partitioned methods for the time-accurate approximation of the evolutionary Stokes–Darcy system

Abstract This paper develops, analyzes and tests a time-accurate partitioned method for the Stokes–Darcy equations. The method combines a time filter and Backward Euler scheme, is second order accurate and provides, at no extra complexity, an estimate of the temporal error. This approach post-processes the solutions of Backward Euler scheme by adding three lines to original codes to increase the time accuracy from first order to second order. We prove long time stability and error estimates of Backward Euler plus time filter with constant time stepsize. Moreover, we extend the approach to variable time stepsize and construct adaptive algorithms. Numerical tests show convergence of our method and support the theoretical analysis.