Mixed Finite Element Analysis of Eigenvalue Problems on Curved Domains

Anahí Dello Russo, Ana E. Alonso
2014 Computational Methods in Applied Mathematics  
A theoretical framework for the analysis of numerical approximations of a particular class of eigenvalue problems by mixed or hybrid methods is presented. More precisely, the eigenproblems considered here can be defined over curved domains or have internal curved boundaries due to the presence of heterogeneities and they may be associated with non compact inverse operators. Sufficient conditions to ensure good convergence properties and optimal error bounds for the external approximations of
more » ... enfunctions/eigenvalues are established. Then, these results are applied to the study of the Stokes eigenvalue problem on a curved non convex two dimensional domain.
doi:10.1515/cmam-2013-0014 fatcat:mihcckjdjjarvbg6zwcj7vjycm