Adaptive time step control for higher order variational time discretizations applied to convection–diffusion–reaction equations

Higher order variational time stepping schemes allow an efficient post-processing for computing a higher order solution. This paper presents an adaptive algorithm whose time step control utilizes the post-processed solution. The algorithm is applied to convection-dominated convection–diffusion–reaction equations. It is shown that the length of the time step properly reflects the dynamics of the solution. With respect to the performance (accuracy, efficiency), the variational time stepping schemes are compared with an adaptive Crank–Nicolson scheme, whose time step control relies on comparing two solutions computed with schemes of the same order.