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We prove first-order convergence of the semi-explicit Euler scheme combinedwith a finite element discretization in space for elliptic-parabolic problemswhich are weakly coupled. This setting includes poroelasticity,thermoelasticity, as well as multiple-network models used in medicalapplications. The semi-explicit approach decouples the system such that eachtime step requires the solution of two small and well-structured linear systemsrather than the solution of one large system. The decoupling improves thecomputational efficiency without decreasing the convergence rates. Thepresented convergence proof is based on an interpretation of the scheme as animplicit method applied to a constrained partial differential equation withdelay term. Here, the delay time equals the used step size. This connectionalso allows a deeper understanding of the weak coupling condition, which weaccomplish to quantify explicitly.

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