Abstract

We study a mixed finite element method for the pseudostress-velocity formulation of the Stokes-Brinkman eigenvalue problem in two and three dimensions, establishing both a priori and a posteriori error estimates. The numerical schemes considered are based on the Raviart-Thomas and Brezzi-Douglas-Marini finite element families. Within the framework of compact operators, we prove convergence and derive optimal a priori error estimates for both eigenvalues and eigenfunctions. In addition, we develop an a posteriori error estimator and show that it is both reliable and efficient. The theoretical results are supported by a series of numerical experiments.