Finite Element Analysis of the Oseen eigenvalue problem
Numerical Analysis
2023-11-10 v1 Numerical Analysis
Abstract
We propose and analyze a finite element method for the Oseen eigenvalue problem. This problem is an extension of the Stokes eigenvalue problem, where the presence of the convective term leads to a non-symmetric problem and hence, to complex eigenvalues and eigenfunctions. With the aid of the compact operators theory, we prove that for inf-sup stable finite elements the convergence holds and hence, error estimates for the eigenvalues and eigenfunctions are derived. We also propose an a posteriori error estimator which results to be reliable and efficient. We report a series of numerical tests in two and three dimension in order to assess the performance of the method and the proposed estimator.
Cite
@article{arxiv.2311.05321,
title = {Finite Element Analysis of the Oseen eigenvalue problem},
author = {Felipe Lepe and Gonzalo Rivera and Jesus Vellojin},
journal= {arXiv preprint arXiv:2311.05321},
year = {2023}
}