20/05/2025, Patrick Farrell: J. Málek & V. Průša, Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids, in Handbook of Mathematical Analysis in Mechanics of Viscous Fluids, Y. Giga & A. Novotný, eds., Springer, Cham (2018), https://doi.org/10.1007/978-3-319-13344-7_1.
06/05/2025, Aaron Baier-Reinio: Srivastava et al., Staggered scheme for the compressible fluctuating hydrodynamics of multispecies fluid mixtures, Physical Review E, 107 (2023), https://doi.org/10.1103/.
29/04/2025, India Marsden: Agelek et al., On Orienting edges of unstructured two- and three-dimensional meshes, ACM Transactions on Mathematical Software, 44 (2017), https://dl.acm.org/doi/abs/10.1145/3061708.
18/03/2025, Alex Ferrer: Baeck et al., A Novel deflation approach for topology optimization and application for optimization of bipolar plates of electrolysis cells, preprint, https://arxiv.org/abs/2406.17491.
11/03/2025, Kars Knook: X. He et al., Immersed finite element methods for parabolic equations with moving interface, Numer. Methods Partial Differential Equations, 29 (2012), https://doi.org/10.1002/num.21722.
18/02/2025, Pablo Brubeck: J. Walkington, A C1 tetrahedral finite element without edge degrees of freedom, SIAM J. Numer. Anal, 52 (2014), https://doi.org/10.1137/130912013.
11/02/2025, Duygu Sap: J. Guzmán and M. Olshanskii, Inf-sup stability of geometrically unfitted Stokes finite elements, Math. Comp., 87 (2017), http://dx.doi.org/10.1090/mcom/3288.
04/02/2025, Boris Andrews: Y. Zhang et al., A MEEVC discretization for two-dimensional incompressible Navier-Stokes equations with general boundary conditions, J. Comp. Phys., 510 (2024), https://doi.org/10.1016/j.jcp.2024.113080.
28/01/2025, Charlie Parker: F. R. A. Aznaran, K. Hu, & C. Parker, Uniformly hp-stable elements for the elasticity complex, preprint, https://arxiv.org/abs/2409.17414.
21/01/2025, Mingong He: Y. Ma, K. Hu, X. Hu, & J. Xu, Robust preconditioners for incompressible MHD models, J. Comp. Phys., 316 (2016), https://doi.org/10.1016/j.jcp.2016.04.019.
03/12/2024, Ioannis P. A. Papadopoulos: L. Banz and A. Schröder, Biorthogonal basis functions in hp-adaptive FEM for elliptic obstacle problems, Comput. Math. Appl., 70 (2015), https://doi.org/10.1016/j.camwa.2015.07.010.
26/11/2024, Pablo Alexei Gazca-Orozco: A. K. Balci, L. Diening, and J. Storn, Relaxed Kačanov scheme for the p-Laplacian with large exponent, SIAM J. Numer. Anal., 61 (2023), https://doi.org/10.1137/22M1528550.
19/11/2024, Patrick Farrell: M. Li et al., Incremental potential contact: intersection-and inversion-free, large-deformation dynamics, ACM Transactions on Graphics, 39 (2020), https://doi.org/10.1145/3386569.3392425.
12/11/2024, Aaron Baier-Reinio: E. Burman and A. Ern, Continuous interior penalty hp-finite element methods for advection and advection-diffusion equations, Math. Comp., 76 (2007), https://doi.org/10.1090/S0025-5718-07-01951-5.
05/11/2024, Umberto Zerbinati: A. Wathen, Some comments on preconditioning for normal equations and least squares, SIAM Rev., 64 (2022), https://doi.org/10.1137/20M1387948.
29/10/2024, Francis Aznaran: C. M. Elliott & T. Ranner, Evolving surface finite element method for the Cahn–Hilliard equation, Numer. Math., 129 (2015), https://doi.org/10.1007/s00211-014-0644-y.
22/10/2024, India Marsden: A. Bock, C. J. Cotter, and R. C. Kirby, Planar curve registration using Bayesian inversion, Comput. Math. Appl., 159 (2024), https://doi.org/10.1016/j.camwa.2024.02.005.
15/10/2024, Pablo Brubeck: J.Guzmán and M. Neilan, Inf-sup stable finite elements on barycentric refinements producing divergence--free approximations in arbitrary dimensions, SIAM J. Numer. Anal., 56 (2018), https://doi.org/10.1137/17M1153467.
04/06/2024, Chalie Parker: L. Chen and X. Huang, Decoupling of mixed methods based on generalized Helmholtz decompositions, SIAM J. Numer. Anal., 56 (2018), https://doi.org/10.1137/17M1145872.
28/05/2024, Kars Knook: N. Spillane, V. Dolean, P. Hauret, F. Nataf, C. Pechstein & R. Scheichl, Abstract robust coarse spaces for systems of PDEs via generalized eigenproblems in the overlaps, Numer. Math., 126 (2014), https://doi.org/10.1007/s00211-013-0576-y.
21/05/2024, Diego Hayashi Alonso: Topology optimisation for transient turbulent compressible flow using an equal-order Discontinuous Galerkin formulation and Runge-Kutta methods.
14/05/2024, Mingdon He: D. A. Arnold, Finite Element Exterior Calculus, Chapters 3 and 4, https://doi.org/10.1137/1.9781611975543.
07/05/2024, India Marsden: S. H. Christiansen, A construction of spaces of compatible differential forms on cellular complexes, Math. Models Methods Appl. Sci., 18 (2008), https://doi.org/10.1142/S021820250800284X.
30/04/2024, Boris Andrews: An overview of compressible Navier-Stokes.
23/04/2024, Patrick Farrell: B. Keith and T. M. Surowiec, Proximal Galerkin: A structure-preserving finite element method for pointwise bound constraints, preprint, https://arxiv.org/abs/2307.12444.
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.
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.