GeoFEM

GeoFEM Homepage

The ERC Starting Project 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 delivered by visitors, collaborators, and occasionally group members. These lectures will have an emphasis on emerging topics and recent advances in finite elements (in a broad sense) for numerical PDEs and Finite Element Exterior Calculus that lack comprehensive documentation, aiming to contribute to broader research contexts, as well as local researchers. Some lectures will include online sessions. To attend remotely, please contact kaibo.hu@ed.ac.uk.


Lectures and Short Courses

  • Riemannian geometry with finite elements
    Evan Gawlik (Santa Clara University), October 11-17, 2025
    Location: Andrew Wiles Building, Oxford
    Abstract: TBA
  • Finite Element Systems
    Snorre Christiansen (University of Oslo), October 6-14, 2025
    Location: Andrew Wiles Building, Oxford
    Abstract: TBA
  • Title TBA
    Ting Lin (Peking University), October 2025
    Location: Andrew Wiles Building, Oxford
    Abstract: TBA
  • 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.