OXFORD FEM READING GROUP

Schedule

23/04/2024, TBA
30/04/2024, TBA
07/05/2024, TBA
14/05/2024, TBA
21/05/2024, TBA
28/05/2024, TBA
04/06/2024, TBA
11/06/2024, TBA

Previous Presentations

05/03/2024, Umberto Zerbinati: A. S. Pechstein and J. Schöberl, The TDNNS method for Reissner–Mindlin plates, Numer. Math., 137 (2017), https://doi.org/10.1007/s00211-017-0883-9.
27/02/2024, Charlie Parker: M. Ainsworth and C. Parker, Computing H2-conforming finite element approximations without having to implement C1-elements, preprint, 2024, https://arxiv.org/abs/2311.04771.
20/02/2024, Aaron Baier-Reinio: A. Ern and D. A. Di Pietro, Mathematical Aspects of Discontinuous Galerkin Methods, Chapter 2, https://doi.org/10.1007/978-3-642-22980-0.
13/02/2024, Pablo Brubeck Martinez: N. Barnafi, L. F. Pavarino, and S. Scacchi, Parallel inexact Newton–Krylov and quasi-Newton solvers for nonlinear elasticity, Comput. Methods Appl. Mech. Engrg., 400 (2022), https://doi.org/10.1016/j.cma.2022.115557.
06/02/2024, Pablo Alexei Gazca-Orozco: A. Ern and J. L. Guermond, Finite Elements III: First-Order and Time-Dependent PDEs, Chapter 71, https://doi.org/10.1007/978-3-030-57348-5.
30/01/2024, Ioannis P. A. Papadopoulos: C. Schwab, p- and hp- Finite Element Methods.
23/01/2024, Alex Ferrer: T. J. R. Hughes, G. Scovazzi, and L. P. Franca, Multiscale and Stabilized Methods, Encyclopedia of computational mechanics second edition, 2018, https://doi.org/10.1002/9781119176817.ecm2051
16/01/2024, Charlie Parker: A. Ern and J. L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs, Chapters 34 and 52.2, https://doi.org/10.1007/978-3-030-56923-5.
05/12/2023, Umberto Zerbinati: D. Boffi, F. Brezzi, and M. Fortin, Mixed Finite Element Methods and Applications, Chapter 6.5, https://doi.org/10.1007/978-3-642-36519-5.
28/11/2023, Umberto Zerbinati: A. Ern and J. L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs, Chapters 46-47, https://doi.org/10.1007/978-3-030-56923-5.
21/11/2023, Francis Aznaran: A. Ern and J. L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs, Chapters 39, https://doi.org/10.1007/978-3-030-56923-5.
14/11/2023, India Marsden: Finite Elements I: Approximation and Interpolation, Chapters 5-7 https://doi.org/10.1007/978-3-030-56341-7.
07/11/2023, Umberto Zerbinati: A. Ern and J. L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs, Chapters 46-47, https://doi.org/10.1007/978-3-030-56923-5.
24/10/2023, Boris Andrews: A. Ern and J. L. Guermond, Finite Elements I: Approximation and Interpolation, Chapters 1-4, https://doi.org/10.1007/978-3-030-56341-7.
17/10/2023, Aaron Baier-Reinio: A. Ern and J. L. Guermond, Finite Elements II: Galerkin Approximation, Elliptic and Mixed PDEs, Chapter 25 and Appendix C, https://doi.org/10.1007/978-3-030-56923-5.
10/10/2023, Pablo Brubeck Martinez: R. C. Kirby, From Functional Analysis to Iterative Methods, SIAM Rev., 52 (2010), https://doi.org/10.1137/070706914.
03/10/2023, Charlie Parker: I. Babuška, A. Craig, J. Mandel, and J. Pitkäranta, Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions, SIAM J. Numer. Anal., 28 (1991), https://doi.org/10.1137/0728034.
For presentations before 3/10/2023, see Francis Aznaran's webpage.

Suggested Papers

B. Grimmer, Provably Faster Gradient Descent via Long Steps, preprint (2023), arXiv:2307.06324.
E. Bueler, The full approximation storage multigrid scheme: A 1D finite element example, preprint (2021), arXiv:2101.05408.
E. Zampa, A Alonso Rodríguez, and F. Rapetti, Using the FES framework to derive new physical degrees of freedom for finite element spaces of differential forms, Adv. Comput. Math., 49 (2023), https://doi.org/10.1007/s10444-022-10001-3.
J. Guzmán and M. Neilan, Conforming and divergence-free Stokes elements on general triangular meshes, Math. Comp., 83 (2014), https://doi.org/10.1090/S0025-5718-2013-02753-6.
A. Angoshtari and A. Yavari, Hilbert complexes of nonlinear elasticity, Z. Angew. Math. Phys., 67 (2016), https://doi.org/10.1007/s00033-016-0735-y.
B. Cockburn, J. Gopalakrishnan, and R. Lazarov, Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems, SIAM J. Numer. Anal., 47 (2009), https://doi.org/10.1137/070706616.
H. Liu, M. Neilan, M. Baris Otus, A divergence-free finite element method for the Stokes problem with boundary correction, J. Numer. Math. 31 (2023), https://doi.org/10.1515/jnma-2021-0125.
M. Neilan and B. Otus, Divergence-free Scott--Vogelius Elements on Curved Domains, SIAM J. Numer. Anal., 59 (2021), https://doi.org/10.1137/20M1360098.
K. Kean, M. Neilan, and M. Schneier, The Scott–Vogelius method for the Stokes problem on anisotropic meshes, Int. J. Numer. Anal. Mod., 19 (2022), http://global-sci.org/intro/article_detail/ijnam/20475.html.
D. N. Arnold, F. Brezzi, B. Cockburn, and L. D. Marini, Unified analysis of discontinuous Galerkin methods for elliptic problems, SIAM J. Numer. Anal., 39 (2002), https://doi.org/10.1137/S003614290138416.
D. Arnold, R. Falk, and R. Winther, Preconditioning in H(div) and applications, Math. Comp., 66 (1997), https://doi.org/10.1090/S0025-5718-97-00826-0.
M. Neilan and M. Wu, Discrete Miranda–Talenti estimates and applications to linear and nonlinear PDEs, J. Comput. Appl. Math., 356 (2019), https://doi.org/10.1016/j.cam.2019.01.032.
J. Xu, The method of subspace corrections, J. Comput. Appl. Math., 128 (2001), https://doi.org/10.1016/S0377-0427(00)00518-5.
X. Hu, J. Zu, and L. T. Zikatanov, Randomized and fault-tolerant method of subspace corrections, Res. Math. Sci., 6 (2019), https://doi.org/10.1007/s40687-019-0187-z.
C. Ortner and E. Süli, Discontinuous Galerkin finite element approximation of nonlinear second-order elliptic and hyperbolic systems, SIAM J. Numer. Anal., 45 (2007), https://doi.org/10.1137/06067119X.
M. Holst and A. Stern, Geometric variational crimes: Hilbert complexes, finite element exterior calculus, and problems on hypersurfaces, Found. Comput. Math., 12( 2012), https://doi.org/10.1007/s10208-012-9119-7.
M. Holst and A. Stern, Semilinear mixed problems on Hilbert complexes and their numerical approximation, Found. Comput. Math., 12 (2012), https://doi.org/10.1007/s10208-011-9110-8.
T. J. Hughes, J. A. Cottrell, and Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194 (2005), https://doi.org/10.1016/j.cma.2004.10.008.
A. Buffa, J. Dölz, S. Kurz, S. Schöps, R. Vázquez, and F. Wolf, Multipatch approximation of the de Rham sequence and its traces in isogeometric analysis, Numer. Math., 144 (2020), https://doi.org/10.1007/s00211-019-01079-x.
C. Carstensen, Clément Interpolation and Its Role in Adaptive Finite Element Error Control, in Partial Differential Equations and Functional Analysis, Operator Theory: Advances and Applications 168, E. Koelink, J. van Neerven, B. de Pagter G. Sweers, A. Luger, H. Woracek, eds, vol 168, Birkhäuser, Basel, 2006, pp. 27-43, https://doi.org/10.1007/3-7643-7601-5_2.
L. Allen and R. C. Kirby, Bounds-constrained polynomial approximation using the Bernstein basis, Numer. Math.k, 152 (2022), https://doi.org/10.1007/s00211-022-01311-1.
B. Cockburn and S. Xia, An adjoint-based super-convergent Galerkin approximation of eigenvalues, J. Comput. Phys., 449 (2022), https://doi.org/10.1016/j.jcp.2021.110816.