Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems

2018/05/23 by Gedicke, Joscha, Khan, Arbaz · 3 citations
#65N15 #65N25 #65N30 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1805.08981

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.

Cited by

• The discontinuous Galerkin method for the Oseen eigenvalue problem
• Discontinuous Galerkin approximation for a Stokes-Brinkman-type formulation for the eigenvalue problem in porous media
• A Stokes-Brinkman-type formulation for the eigenvalue problem in porous media

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