A posteriori error estimates of stabilized low-order mixed finite elements for the Stokes eigenvalue problem

Abstract

In this paper we obtain a priori and a posteriori error estimates for stabilized low-order mixed finite element methods for the Stokes eigenvalue problem. We prove the convergence of the method and a priori error estimates for the eigenfunctions and the eigenvalues. We define an error estimator of the residual type which can be computed locally from the approximate eigenpair and we prove that, up to higher order terms, the estimator is equivalent to the energy norm of the error. We also present some numerical tests which show the performance of the adaptive scheme.