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arXiv · 2211.08961

First-order system least-squares finite element method for singularly perturbed Darcy equations

Thomas Führer·Juha Videman
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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.

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Thomas Führer, Juha Videman. 2022-11-16. First-order system least-squares finite element method for singularly perturbed Darcy equations. https://arxiv.org/abs/2211.08961

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