| Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
|---|---|---|
| Page(s) | 2283 - 2300 | |
| DOI | https://doi.org/10.1051/m2an/2023049 | |
| Published online | 03 July 2023 | |
First-order system least-squares finite element method for singularly perturbed Darcy equations
1
Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Santiago, Chile
2
CAMGSD/Departamento de Matemática, Instituto Superior Técnico, Universidade de Lisboa, 1049-001 Lisbon, Portugal
* Corresponding author: tofuhrer@mat.uc.cl
Received:
16
November
2022
Accepted:
23
May
2023
We define and analyse a least-squares finite element method for a first-order reformulation of a scaled Brinkman model of fluid flow through porous media. We introduce a pseudostress variable that allows to eliminate the pressure variable from the system. It can be recovered by a simple post-processing. It is shown that the least-squares functional is uniformly equivalent, i.e., independent of the singular perturbation parameter, to a parameter dependent norm. This norm equivalence implies that the least-squares functional evaluated in the discrete solution provides an efficient and reliable a posteriori error estimator. Numerical experiments are presented.
Mathematics Subject Classification: 65N30 / 65N12
Key words: Least-squares finite element method / Brinkman equation / Darcy equations / Singularly perturbed problem / First-order formulation
© The authors. Published by EDP Sciences, SMAI 2023
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