Semi-explicit discretization schemes for weakly coupled elliptic-parabolic problems
Journal article, 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

Author

R. Altmann

University of Augsburg

Roland Maier

University of Gothenburg

Chalmers, Mathematical Sciences, Applied Mathematics and Statistics

B. Unger

University of Stuttgart

Technische Universität Berlin

Mathematics of Computation

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

Vol. 90 329 1089-1118

Subject Categories

Computational Mathematics

Control Engineering

Mathematical Analysis

DOI

10.1090/mcom/3608

More information

Latest update

7/3/2024 2