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arXiv · 1805.08981

Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems

Joscha Gedicke·Arbaz Khan
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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.

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Joscha Gedicke, Arbaz Khan. 2018-05-23. Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems. https://arxiv.org/abs/1805.08981

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