GeoFEM

The ERC Starting Grant GeoFEM (Geometric Finite Element Methods) investigates discretization of geometric objects with finite elements, connections between finite elements and discrete differential geometry, and applications.

GeoFEM will host lectures and short courses given by visitors and collaborators.

Lectures and Short Courses

• Spectral Theory and Spectral Practice
  Umberto Zerbinati (University of Oxford), May 2025
  Course Website: https://www.uzerbinati.eu/teaching/spectral_theory/
  Location: James Clerk Maxwell Building (JCMB) 5328 (May 13, 14), JCMB 5326 (May 16)
  Time: May 13, 2025, 10:00 AM - 12:00 PM; May 14, 2025, 2:00 PM - 4:00 PM; May 16, 2025, 3:00 PM - 5:00 PM
  Show Abstract
  This short course explores finite element discretisations of eigenvalue problems involving non-normal operators, with a focus on the advection-diffusion equation as a guiding example. We begin by revisiting fundamental spectral notions—self-adjointness, normality, spectra, and pseudospectra—with particular emphasis on how an operator spectrum informs us about the physical behaviour of the time-dependent PDEs. The core of the course is devoted to the classical analysis of finite element approximations: we present in detail the Bramble-Osborn results for non-self-adjoint eigenvalue problems, including full proofs, and discuss their implications for convergence and approximation quality. For comparison, we also review the celebrated Babuška-Osborn theory in the self-adjoint case. If time permits, we will conclude with a discussion on iterative solvers and preconditioning strategies tailored to non-normal eigenvalue problems. The course requires basic background in functional analysis and finite element methods.