A Posteriori Error Estimates of stabilized Low-Order Mixed Finite Elements for the Stokes Eigenvalue Problem

MARÍA G. ARMENTANO, VERÓNICA MORENO

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2014 vol. 269 p. 132 - 149

0377-0427

In this paper we obtain a priori and a posteriori error estimates for stabilized low-ordermixed 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.