First-order system least-squares finite element method for singularly perturbed Darcy equations
Numerical Analysis
2022-11-17 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.2211.08961,
title = {First-order system least-squares finite element method for singularly perturbed Darcy equations},
author = {Thomas Führer and Juha Videman},
journal= {arXiv preprint arXiv:2211.08961},
year = {2022}
}