GeoFEM

GeoFEM Homepage

The ERC Starting Project GeoFEM (Geometric Finite Element Methods) explores the discretization of geometric objects using finite element methods, connections between finite elements and discrete differential geometry, and their applications.

GeoFEM hosts lectures and short courses delivered by visitors, collaborators, and occasionally group members. These sessions focus on emerging topics and recent advances in finite element methods (broadly defined) and Finite Element Exterior Calculus, particularly those lacking comprehensive documentation, to contribute to broader research contexts and support local researchers. Some lectures offer online participation. 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
  • A Posteriori Error Estimation by Preconditioning
    Yuwen Li (Zhejiang University), August 4–8, 2025
    Location: James Clerk Maxwell Building (JCMB), Edinburgh. August 7, 13:30–15:30: JCMB 6206; August 8, 13:30–15:30: JCMB 6201; August 11, 13:30–15:30: JCMB 6206
    Abstract: Show Abstract
    This short course explores preconditioning and a posteriori error estimation in finite element methods, focusing on H(curl) and H(div) spaces. We begin by reviewing fundamental concepts in a posteriori error estimates for adaptive methods and iterative solvers for linear algebraic systems. The course emphasizes the interplay between iterative solvers and a posteriori error estimates, demonstrating the derivation of novel parameter-robust and p-robust error estimators in H(curl) and H(div) using nodal auxiliary space preconditioning at the continuous level. For comparison, we also examine classical a posteriori error analysis in H(grad), H(curl), and H(div).
  • Spectral Theory and Spectral Practice
    Umberto Zerbinati (University of Oxford), May 13–16, 2025
    Course Website: https://www.uzerbinati.eu/teaching/spectral_theory/
    Location: James Clerk Maxwell Building (JCMB) 5328 (May 13–14), JCMB 5326 (May 16), Edinburgh
    Time: May 13, 2025, 10:00–12:00; May 14, 2025, 14:00–16:00; May 16, 2025, 15:00–17:00
    Show Abstract
    This short course explores finite element discretizations 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’s spectrum informs the physical behavior of time-dependent PDEs. The core of the course is devoted to the classical analysis of finite element approximations: we present 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 for self-adjoint cases. If time permits, we will conclude with a discussion on iterative solvers and preconditioning strategies tailored to non-normal eigenvalue problems. The course requires a basic background in functional analysis and finite element methods.