Divergence-conforming discontinuous Galerkin finite elements for Stokes eigenvalue problems
This work addresses the need for accurate and reliable numerical methods for Stokes eigenvalue problems in computational fluid dynamics.
The paper develops a divergence-conforming discontinuous Galerkin method for Stokes eigenvalue problems, providing a priori error estimates and a robust a posteriori error estimator, with numerical examples confirming convergence and estimator reliability.
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.