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AMCS Seminar: Adaptive finite element method for the Maxwell eigenvalue problem

Start Date: December 10, 2018
End Date: December 10, 2018

By Prof. Daniele Boffi (University of Pavia, Italy)
 
The Maxwell eigenvalue problem has always been a challenging research area for numerical analysts. The a priori error analysis for its finite element approximation is nowadays a well-understood and classical topic, including its several variations (h-version, p-version, discontinuous Galerkin, regularized and penalty formulations, etc.). The fundamental tools (sometimes behind the scenes, but always present) for the study of this problem are related to mixed finite elements and, in particular, to de Rham complex and discrete differential forms. Taking advantage of this remark, we consider the a posteriori analysis and the associate adaptive finite element scheme. We prove the convergence with optimal rate for the edge finite element adaptive approximation of the Maxwell eigenvalue problem. In three dimensions, the result is not a trivial extension of the analysis previously performed for the approximation of the Laplace eigenproblem in mixed form. Particular attention is devoted to the case of multiple eigenvalues and clusters of eigenvalues. 

Bio: Daniele Boffi is Professor of Numerical Analysis at the Department of Mathematics of the University of Pavia, Italy, since 2005. He is adjunct professor at the Department of Mathematics and System Analysis, Aalto University, Finland, since 2017. He received a PhD in Mathematics from the Universities of Brescia-Milano-Pavia, Italy, in 1996. He has been visitor professor at several institutions. He is the Director of the PhD Higher Education School of the University of Pavia, Italy, since 2015. His primary research interests are related to the numerical approximation of partial differential equations, including mixed finite elements, eigenvalue problems, computational electromagnetism, interaction of fluids and solids.
 

More Information:

For more info contact: Prof. Peter A. Markowich : email: Peter.Markowich@kaust.edu.sa
 
Date: Monday 10th Dec 2018
Time:12:00 PM - 01:00 PM
Location: Bldg. 3 level 5 Rm. 5209
Refreshments: Light lunch will be served