Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems

We prove first-order convergence of the semi-explicit Euler scheme combined with a finite element discretization in space for elliptic-parabolic problems which are weakly coupled. This setting includes poroelasticity, thermoelasticity, as well multiple-network models used medical applications. The approach decouples system such that each time step requires solution two small and well-structured linear systems rather than one large system. decoupling improves computational efficiency without decreasing rates. presented proof is based on an interpretation implicit method applied to constrained partial differential equation delay term. Here, equals size. connection also allows deeper understanding weak coupling condition, we accomplish quantify explicitly.