SEMINAIRE D'ANALYSE NUMERIQUE
Année universitaire 2016-2017
Jeudi 15 septembre 2016
Daniele
BOFFI (Dipartimento di Matematica "F. Casorati",
Università di Pavia, Italie)
A posteriori error analysis for the Maxwell
eigenvalue problem
A posteriori error analysis for eigenvalue problems raises interesting
questions, which have received partial answers only recently.
A fundamental issue concerns how to design adaptive schemes for the
approximation of multiple eigenvalues or when clusters of eigenvalues are
present. The convergence and quasi-optimality of the adaptive approximation
of the Laplace eigenvalue problem in mixed form has been recently studied
(joint work with D. Gallist, F. Gardini, and L. Gastaldi). The analysis is
cluster robust and makes use of standard finite element schemes based on
Raviart-Thomas element in two and three space dimensions. The equivalence
with a suitable eigenvalue problem in mixed form suggests how to extend the
result from mixed Laplacian to the Maxwell eigenvalue problem (joint work
with L. Gastaldi, R. Rodriguez, and I. Sebestova).
