Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems
Numerical Analysis
2018-05-24 v1
Abstract
In this paper, we present a divergence-conforming discontinuous Galerkin finite element method for Stokes eigenvalue problems. We prove a priori error estimates for the eigenvalue and eigenfunction errors and present a robust residual based a posteriori error estimator. The a posteriori error estimator is proven to be reliable and (locally) efficient in a mesh-dependent velocity-pressure norm. We finally present some numerical examples that verify the a priori convergence rates and the reliability and efficiency of the residual based a posteriori error estimator.
Cite
@article{arxiv.1805.08981,
title = {Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems},
author = {Joscha Gedicke and Arbaz Khan},
journal= {arXiv preprint arXiv:1805.08981},
year = {2018}
}