Homepage for the University of Oxford finite element methods reading group!
Meetings this academic year will be hosted on Fridays from 15:00–16:00 GMT, in S2.37 (when available). You can join on Teams by clicking here, or using the details:
2025–2026
Trinity term
| Week | Date | Topic | Presenter |
|---|---|---|---|
| 1 | 01.MAY | TBA… | TBA… |
| 2 | 08.MAY | TBA… | TBA… |
| 3 | 15.MAY | TBA… | TBA… |
| 4 | 22.MAY | TBA… | TBA… |
| 5 | 29.MAY | TBA… | TBA… |
| 6 | 05.JUN | (Break…) | |
| 7 | 12.JUN | TBA… | TBA… |
| 8 | 19.JUN | TBA… | TBA… |
While the schedule for trinity term isn’t yet finalised, we may likely be on hiatus for the first half, since many of us will be at the Programme on Differential Complexes at the University of Vienna.
Click here to view references for upcoming presentations.
Click here to hide the records of past presentations.
–2025
For prior years, see Charlie Parker’s page here.
2025–2026
Michaelmas term
| Week | Date | Topic | Presenter |
|---|---|---|---|
| 1 | 17.OCT | Long steps in gradient descent methods (Grimmer, 2024; Zhigljavsky, Pronzato & Bukina, 2013) | Me (Boris Andrews) |
| 2 | 24.OCT | Sparse direct solvers (Duff, Erisman & Reid, 2017) | Kars Knook |
| 3 | 31.OCT | Group meeting | Everyone |
| 4 | 07.NOV | Preconditioners for PDE timesteppers (Southworth et al., 2022) | Charlie Parker |
| 5 | 14.NOV | From classical thermodynamics to fluid motion (Málek & Průša, 2018) | Jakub Cach |
| 6 | 21.NOV | Turbulence (Layton, 2018) | Mingdong He |
| 7 | 28.NOV | (Break…) | |
| 8 | 05.DEC | Grad–Shafranov: MHD equilibria and how to find them (Schnack, 2009; He et al., 2025; Blickhan, Stratton & Kaptanoglu, 2025) | Tom Higham |
Hilary term
| Week | Date | Topic | Presenter |
|---|---|---|---|
| 1 | 23.JAN | Differential forms and virtual elements (Arnold, 2018; Beirao da Veiga et al., 2023) | Olav Tyssvang |
| 2 | 30.JAN | Finding equilibria of Hamiltonian systems (Bressan et al., 2025; Bressan et al., 2018) | Mingdong He |
| 3 | 06.FEB | Mollifiers & applications in FEMs (Evans, 2010) | Me (Boris Andrews) |
| 4 | 13.FEB | Free-boundary and two-phase MHD (Gerbeau, Le Bris & Lelièvre, 2006; Gu, Luo & Zhang, 2024) | Ganghui Zhang |
| 5 | 20.FEB | (Break…) | |
| 6 | 27.FEB | Distributional elements (Braess & Schöberl, 2008; Christiansen, 2011) | Yizhou Liang |
| 7 | 06.MAR | Unfitted FEM (Nitsche, 1972; Hansbo & Hansbo, 2002; Burman, 2010; Burman et al., 2025) | Xinpei Zhang |
| 8 | 13.MAR | Contact manifolds (Arnold, 1989; Rumin, 1994) | Yuechen Zhu |
Slides and notes can be found, when available, by clicking the topic titles.
Click here to hide references for upcoming presentations.
2025–2026
Michaelmas term
T. Blickhan, J. Stratton and A. A. Kaptanoglu, MRX: A differentiable 3D MHD equilibrium solver without nested flux surfaces, arXiv (2025), doi:10.48550/arXiv.2510.26986
I. S. Duff, A. M. Erisman and J. K. Reid, Direct Methods for Sparse Matrices. Oxford University Press, 2017
B. Grimmer, Provably faster gradient descent via long steps, SIAM Journal on Optimization, 34 (2024), doi:10.1137/23M1588408
M. He, P. E. Farrell, K. Hu and B. D. Andrews, Helicity-preserving finite element discretization for magnetic relaxation, arXiv (2025), doi:10.48550/arXiv.2501.11654
W. Layton, Introduction to the Numerical Analysis of Incompressible Viscous Flows. SIAM, 2018
J. Málek and V. Průša, Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids. In Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham, 2018. doi:10.1007/978-3-319-13344-7_1
D. D. Schnack, Lectures in Magnetohydrodynamics. Springer, 2009
B. S. Southworth, O. Krzysik, W. Pazner and H. De Sterck, Fast solution of fully implicit Runge–Kutta and discontinuous Galerkin in time for numerical PDEs, part I: The linear setting, SIAM Journal on Scientific Computing, 44 (2022), doi:10.1137/21M1389742
A. Zhigljavsky, L. Pronzato and E. Bukina, An asymptotically optimal gradient algorithm for quadratic optimization with low computational cost, Optimization Letters, 7 (2013), doi:10.1007/s11590-012-0491-7
Hilary term
D. Arnold, Finite Element Exterior Calculus. SIAM, 2018
V. I. Arnold, Mathematical Methods of Classical Mechanics. Springer, 1989
L. Beirao Da Veiga, F. Brezzi, D. Marini and A. Russo, The virtual element method, Acta Numerica (2023) doi:10.1017/S0962492922000095
D. Braess and J. Schöberl, Equilibrated residual error estimator for edge elements, Mathematics of Computation, 77.262 (2008), doi:10.1090/S0025-5718-07-02080-7
C. Bressan, M. Kraus, O. Maj and P. J. Morrison, Metriplectic relaxation to equilibria, arXiv (2025), doi:10.48550/arXiv.2506.09787
C. Bressan, M. Kraus, P. J. Morrison and O. Maj, Relaxation to magnetohydrodynamics equilibria via collision brackets, Journal of Physics: Conference Series, 1125 (2018), doi:10.1088/1742-6596/1125/1/012002
E. Burman, Ghost penalty, Comptes Rendus Mathématique, 348.21–22 (2010), doi:10.1016/j.crma.2010.10.006
E. Burman, P. Hansbo, M. G. Larson and S. Zahedi, Cut finite element methods, Acta Numerica, 34 (2025), doi:10.1017/S0962492925000017
S. H. Christiansen, On the linearization of Regge calculus, Numerische Mathematik, 119.4 (2011), doi:10.1007/s00211-011-0394-z
L. C. Evans, Partial Differential Equations. AMS, 2010
J.-F. Gerbeau, C. Le Bris and T. Lelièvre, Mathematical Methods for the Magnetohydrodynamics of Liquid Metals. Clarendon Press, 2006
X. Gu, C. Luo and J. Zhang, Local well-posedness of the free-boundary incompressible magnetohydrodynamics with surface tension, Journal de Mathématiques Pures et Appliquées (2024) doi:10.1016/j.matpur.2023.12.009
A. Hansbo and P. Hansbo, An unfitted finite element method, based on Nitsche’s method, for elliptic interface problems, Computer Methods in Applied Mechanics and Engineering, 191.47–48 (2002), doi:10.1016/S0045-7825(02)00524-8
J. Nitsche, On Dirichlet problems using subspaces with nearly zero boundary conditions, in The Mathematical Foundations of the Finite Element Method with Applications to Partial Differential Equations. Academic Press, 1972
M. Rumin, Formes différentielles sur les variétés de contact, Journal of Differential Geometry, 39.2 (1994), doi:10.4310/jdg/1214454873
Click here to view the list of suggested papers.