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This paper is concerned with global-in-time, nonoverlapping domaindecomposition methods for the mixed formulation of the diffusion problem. Twoapproaches are considered: one uses the time-dependent Steklov-Poincar\'eoperator and the other uses Optimized Schwarz Waveform Relaxation (OSWR) basedon Robin transmission conditions. For each method, a mixed formulation of aninterface problem on the space-time interfaces between subdomains is derived,and different time grids are employed to adapt to different time scales in thesubdomains. Demonstrations of the well-posedness of the subdomain problemsinvolved in each method and a convergence proof of the OSWR algorithm are givenfor the mixed formulation. Numerical results for 2D problems with strongheterogeneities are presented to illustrate the performance of the two methods.

Space-Time Domain Decomposition Methods for Diffusion Problems in Mixed Formulations