Pseudostress‐Based Velocity Formulation for the Stokes‐Brinkman‐Type Eigenvalue Problem: A Priori and a Posteriori Error Analysis

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.