First-order system least-squares finite element method for singularly perturbed Darcy equations
Year: 2022
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Führer, Thomas, Videman, Juha
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4320560908