Abstract
In many fields of applications such as reactive transport or ocean-atmosphere coupling, models with very different spatial and time scales have to be coupled. Optimized Schwarz Waveform Relaxation methods (OSWR), applied to linear advection-reaction-diffusion problems in [1, 8], provide efficient solvers for this purpose. They have two main advantages: first, they are global in time and thus permit non conforming space-time discretization in different subdomains, and second, few iterations are needed to compute an accurate solution, due to optimized transmission conditions. It has been proposed in [4] to use a discontinuous Galerkin method in time as a subdomain solver. Rigorous analysis can be made for any degree of accuracy and local time-stepping, and finally time steps can be adaptively controlled by a posteriori error analysis, see [6, 7, 10].
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