| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 1921 - 1952 | |
| DOI | https://doi.org/10.1051/m2an/2023033 | |
| Published online | 03 July 2023 | |
A posteriori error estimation and adaptivity for multiple-network poroelasticity
1
Institute of Basal Medical Sciences, University of Oslo, Oslo, Norway
2
Department of Scientific Computing and Numerical Analysis, Simula Research Laboratory, Oslo, Norway
3
Department of Mathematics, University of Bergen, Bergen, Norway
4
Department of Mathematics and Statistics, Texas Tech University, Lubbock, Texas, United States
* Corresponding author: travis.thompson@ttu.edu
Received:
14
December
2021
Accepted:
14
April
2023
The multiple-network poroelasticity (MPET) equations describe deformation and pressures in an elastic medium permeated by interacting fluid networks. In this paper, we (i) place these equations in the theoretical context of coupled elliptic–parabolic problems, (ii) use this context to derive residual-based a posteriori error estimates and indicators for fully discrete MPET solutions and (iii) evaluate the performance of these error estimators in adaptive algorithms for a set of test cases: ranging from synthetic scenarios to physiologically realistic simulations of brain mechanics.
Mathematics Subject Classification: 65M50 / 65M60 / 65Z05 / 92-08
Key words: Multiple network poroelasticity / a posteriori error estimates / adaptive finite element method / brain modeling
© The authors. Published by EDP Sciences, SMAI 2023
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