Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems
Artikel i vetenskaplig tidskrift, 2021

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 as multiple-network models used in medical applications. The semi-explicit approach decouples the system such that each time step requires the solution of two small and well-structured linear systems rather than the solution of one large system. The decoupling improves the computational efficiency without decreasing the convergence rates. The presented convergence proof is based on an interpretation of the scheme as an implicit method applied to a constrained partial differential equation with delay term. Here, the delay time equals the used step size. This connection also allows a deeper understanding of the weak coupling condition, which we accomplish to quantify explicitly.

poroelasticity

semi-explicit time discretization

Elliptic-parabolic problem

multiple-network

delay

Författare

R. Altmann

Universität Augsburg

Roland Maier

Göteborgs universitet

Chalmers, Matematiska vetenskaper, Tillämpad matematik och statistik

B. Unger

Universität Stuttgart

Technische Universität Berlin

Mathematics of Computation

0025-5718 (ISSN) 1088-6842 (eISSN)

Vol. 90 329 1089-1118

Ämneskategorier

Beräkningsmatematik

Reglerteknik

Matematisk analys

DOI

10.1090/mcom/3608

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Senast uppdaterat

2024-07-03