Defect corrected averaging for parabolic PDEs

We consider parabolic partial differential equations with highly oscillatory source terms. The timescale of the problem is assumed to be much larger than the timescale of the oscillation. Resolution of the smallest timescale constitutes a strong restriction on the stepsize of time integration method. Averaging techniques like stroboscopic averaging have been developed to overcome this restriction. In case of parabolic equations these techniques are of limited advantage. We have developed defect corrected averaging techniques that allow timesteps taylored to the timescale of diffusion. They are based on Krylov subspace iterations for the abstract solution operator of the system. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)