Adaptive Mixed Finite Element Approximation of Eigenvalue Clusters

Thursday, October 23, 2014 - 3:40pm - 4:25pm
Keller 3-180
Daniele Boffi (Università di Pavia)
The analysis of adaptive finite element methods for the approximation of partial differential equations is well established and has been successfully applied to a variety of problems (ranging from source problems to eigenvalue problems).
In the framework of eigenvalue problems, we review the main issues related to the approximation of multiple eigenvalues. In particular, we show that an optimal strategy should consider an error indicator based on all discrete eigenfunctions approximating a multidimensional eigenspace. This situation extends to clusters of eigenvalues, meaning that if two continuous eigenvalues are very close to each other then, numerically, they have to be considered together.
Our main contribution consists in developing and analyzing ad adaptive strategy for the approximation of the eigensolution of eigenvalue problems in mixed form. Our theory is cluster robust, in the sense that it allows for the simultaneous approximation of the eigenvalues belonging to the same cluster.
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