A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
Numerical Analysis
2025-07-14 v1 Numerical Analysis
Abstract
In this paper we introduce and analyze, for two and three dimensions, a finite element method to approximate the natural frequencies of a flow system governed by the Stokes-Brinkman equations. Here, the fluid presents the capability of being within a porous media. Taking advantage of the Stokes regularity results for the solution, and considering inf-sup stable families of finite elements, we prove convergence together with a priori and a posteriori error estimates for the eigenvalues and eigenfunctions with the aid of the compact operators theory. We report a series of numerical tests in order to confirm the developed theory.
Cite
@article{arxiv.2507.08226,
title = {A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media},
author = {Felipe Lepe and Gonzalo Rivera and Jesus Vellojin},
journal= {arXiv preprint arXiv:2507.08226},
year = {2025}
}