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Internal Seminar Calendar

2025 – 2026

  • 30th Oct 2025 – 10h30 to 12h00 Susanne Claus:
  • 16th Oct 2025 – 10h30 to 12h00 Sébastien Imperiale: Stabilisation of the high-order discretised wave equation for data assimilation problems. (abstract)
  • 18th Sep 2025 – 10h30 to 12h00 Zuodong Wang: Efficient numerical schemes for evolution equations with singularities and shocks. (abstract)

2024 – 2025

  • 24th July 2025 – 10h30 to 12h00 Lukas Renelt: Model order reduction for parametrized PDEs: An introduction & recent advances in the application to Friedrichs’ systems. (abstract)
  • 17th July 2025 – 10h30 to 12h00 Romain Mottier: Hybrid high-order methods for the numerical simulation of elasto-acoustic wave propagation. (abstract)
  • 10th July 2025 – 10h30 to 12h00 Jai Tushar: A discrete trace theory for non-conforming hybrid polytopal discretisation methods with application to analysis of BDDC preconditioners. (abstract)
  • 7th July 2025 – 10h30 to 12h00 Baptiste Plaquevent-Jourdain: A Robust Linearization Method for Complementarity Problems: A Detour Through Hyperplane Arrangements. (abstract)
  • 3rd July 2025 – 10h30 to 12h00 Emile Parolin: Coarse spaces for non-hermitian and indefinite problems using two-level non-hermitian preconditioners. (abstract)
  • 15th May 2025 – 10h30 to 12h00 Daniel Zegarra Vasquez: Efficient numerical simulation of single-phase flow in three-dimensional fractured porous media. (abstract)
  • 27th March 2025 – 10h30 to 12h00 Michel Kern: Geological storage of CO2: an example for the simulation of subsurface flow. (abstract)
  • 20th March 2025 – 10h30 to 12h00 Rekha Khot: Hybrid high-order methods for the wave equation in first-order form. (abstract)
  • 13th March 2025 – 10h30 to 12h00 Simon Lemaire: Building (yet other) bridges between polytopal methods. (abstract)
  • 6th March 2025 – 10h30 to 12h00 Philip Herbert: Shape optimisation using Lipschitz functions. (abstract)
  • 6th February 2025 – 10h00 to 11h30 Martin Licht: Perspectives in structure-preserving numerical schemes. (abstract)
  • 30th January 2025 – 10h30 to 12h00 Divay Garg: Discontinuous Galerkin finite element methods for the control-constrained Dirichlet control problem governed by the diffusion equation. (abstract)
  • 23rd January 2025 – 10h30 to 12h00 Ibtissem Lannabi: Analysis of spurious oscillations problem of Finite Volume Methods for low Mach number flows in fluid mechanics. (abstract)
  • 13th January 2025 – 10h30 to 12h00 Peter Moritz von Schultzendorff: Adaptive homotopy continuation for relative permeability models in reservoir simulation. (abstract)
  • 17th December 2024 – 11h00 to 12h00 Ani Miraçi: Iterative solvers and optimal complexity of adaptive finite element methods. (abstract)
  • 12th December 2024 – 11h00 to 12h00 Lina Zhao: A parameter-free HDG method for linear elasticity with strongly symmetric stress. (abstract)
  • 21st November 2024 – 11h00 to 12h00 Guillaume Bonnet: 𝐻² conforming virtual element discretization of nondivergence form elliptic equations. (abstract)
  • 17 October 2024 – 11h00 to 12h00 Gregor Gantner: Space-time FEM-BEM couplings for parabolic transmission problems. (abstract)
  • 15 October 2024 – 11h00 to 12h00 André Harnist: Robust augmented energy a posteriori estimates for Lipschitz and strongly monotone elliptic problems. (abstract)
  • 10 October 2024 – 11h00 to 12h00 Jørgen S. Dokken: A view into the development of the FEniCS project over two decades. (abstract)
  • 2nd October 2024 – 11h00 to 12h00 Weifeng Qiu: Numerical analysis for incompressible MHD and Maxwell’s transmission eigenvalues and Moving interface without thickness. (abstract)

2023 – 2024

  • 10 September 2024 – 11h00 to 12h00 Carsten Carstensen: Adaptive computation of fourth-order problems. (abstract)
  • 25 April 2024 – 11h00 to 12h00 Martin Werner Licht: Computable reliable bounds for Poincaré–Friedrichs constants via Čech–de-Rham complexes. (abstract)
  • 4 April 2024 – 11h00 to 12h00 Roland Maier: A localized orthogonal decomposition strategy for hybrid discontinuous Galerkin methods. (abstract)
  • 2 April 2024 – 14h00 to 15h00 Andreas Rupp: Homogeneous multigrid for hybrid discretizations: application to HHO methods. (abstract)
  • 18 January 2024 – 14h00 to 15h00 Zoubida Mghazli: Modeling some biological phenomena via the porous media approach. (abstract)
  • 23 November 2023 – 11h00 to 12h00 Olivier Hénot: Computer-assisted proofs of radial solutions of elliptic systems on R^d. (abstract)
  • 16 November 2023 – 17h00 to 18h00 Maxime Theillard: A Volume-Preserving Reference Map Method for the Level Set Representation. (abstract)
  • 13 November 2023 – 11h00 to 12h00 Charles Parker: Implementing $H^2$-conforming finite elements without enforcing $C^1$-continuity. (abstract)
  • 09 November 2023 – 11h00 to 12h00 Maxime Breden: Computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem. (abstract)
  • 10 September 2024 – 11h00 to 12h00 Carsten Carstensen: Adaptive computation of fourth-order problems. (abstract)

2022 – 2023

  • 25 May 2023 – 11h00 to 12h00 Martin Vohralík: A posteriori error estimates robust with respect to nonlinearities and final time. (abstract)
  • 11 May 2023 – 11h00 to 12h00 Konstantin Brenner: On the preconditioned Newton’s method for Richards’ equation. (abstract)
  • 4 May 2023 – 11h00 to 12h00 Ludmil Zikatanov: High order exponential fitting discretizations for convection diffusion problems. (abstract)
  • 23 March 2023 – 11h00 to 12h00 Marien Hanot: Polytopal discretization of advanced differential complexes.(abstract)
  • 9 February 2023 – 11h00 to 12h00 Roland Maier: Semi-explicit time discretization schemes for elliptic-parabolic problems. (abstract)
  • 2 February 2023 – 11h00 to 12h00 Simon Legrand: Parameter studies automation with Prune_rs. (abstract)
  • 28 November 2022 – 11h00 to 12h00 Xuefeng Liu: Guaranteed eigenvalue/eigenfunction computation and its application to shape optimization problems. (abstract)
  • 17 November 2022 – 11h00 to 12h00 Fabio Vicini: Flow simulations on porous fractured media: a small numerical overview from my perspective. (abstract)
  • 20 October 2022 – 10h00 to 11h00 Iuliu Sorin Pop: Non-equilibrium models for flow in porous media. (abstract)
  • 06 October 2022 – 15h00 to 16h00 Rekha Khot: Nonconforming virtual elements for the biharmonic equation with Morley degrees of freedom on polygonal meshes. (abstract)

2021 – 2022

  • 21 September 2022 – 15h00 to 16h00 Alexandre IMPERIALE: Numerical methods for time domain wave propagation problems applied to ultrasonic testing modelling. (abstract)
  • 16 June 2022 – 11h30 to 12h30 Cherif Amrouche: Elliptic Problems in Lipschitz and in $C^{1,1}$ Domains. (abstract)
  • 13 June 2022 – 11h00 to 12h00 Jean-Luc Guermond: Invariant-domain preserving IMEX time stepping methods. (abstract)
  • 5 May 2022 – 11h00 to 12h00 Daniel Zegarra Vasquez: Simulation d’écoulements monophasiques en milieux poreux fracturés par la méthode des éléments finis mixtes hybrides. (abstract)
  • 19 April 2022 – 14h00 to 15h00 Christos Xenophontos: Finite Element approximation of singularly perturbed eigenvalue problems. (abstract)
  • 14 April 2022 – 11h00 to 12h00: Idrissa Niakh: Stable model reduction for linear variational inequalities with parameter-dependent constraints. (abstract)
  • 7 April 2022 – 17h00 to 18h00: Christoph Lehrenfeld: Embedded Trefftz Discontinuous Galerkin methods. (abstract)
  • 24 March 2022 – 11h00 to 12h00: Miloslav Vlasak: A posteriori error estimates for discontinuous Galerkin method. (abstract)
  • 10 March 2022 – 11h00 to 12h00: Ruma Maity: Parameter dependent finite element analysis for ferronematics solutions. (abstract)
  • 3 February 2022 – 11h00 to 12h00: Pierre Matalon: An h-multigrid method for Hybrid High-Order discretizations of elliptic equations. (abstract)
  • 27 January 2022 – 11h00 to 12h00: Frédéric Lebon: On the modeling of nonlinear imperfect solid/solid interfaces by asymptotic techniques. (abstract)
  • 20 January 2022 – 11h00 to 12h00: Isabelle Ramière: Automatic multigrid adaptive mesh refinement with controlled accuracy for quasi-static nonlinear solid mechanics. (abstract)
  • 13 January 2022 – 11h00 to 12h00: Koondanibha Mitra: A posteriori estimates for nonlinear degenerate parabolic and elliptic equations. (abstract)
  • 10 December 2021 – 11h00 to 12h00: Gregor Gantner: Applications of a space-time first-order system least-squares formulation for parabolic PDEs. (abstract)
  • 25 November 2021 – 11h00 to 12h00: Pierre Gosselet: Asynchronous Global/Local coupling. (abstract)
  • 24 November 2021 – 10h30 to 11h30: Grégory Etangsale: A primal hybridizable discontinuous Galerkin method for modelling flows in fractured porous media. (abstract)

2020 – 2021

  • 06 September 2021 – 15h00 to 16h00: Rolf Stenberg: Nitsche’s Method for Elastic Contact Problems. (abstract)
  • 17 June 2021 – 11h00 to 12h00: Elyes Ahmed: Adaptive fully-implicit solvers and a posteriori error control for multiphase flow with wells. (abstract)
  • 3 June 2021 – 11h00 to 12h00: Oliver Sutton: High order, mesh-based multigroup discrete ordinates schemes for the linear Boltzmann transport problem. (abstract)
  • 29 April 2021 – 11h00 to 12h00: Lorenzo Mascotto: Enriched nonconforming virtual element methods (abstract)
  • 1 April 2021 – 11h00 to 12h00: André Harnist : Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems (abstract)
  • 11 March 2021 – 15h00 to 16h00: Omar Duran : Explicit and implicit hybrid high-order methods for the wave equation in time regime (abstract)
  • 25 February 2021 – 14h00 to 15h00: Buyang Li : A bounded numerical solution with a small mesh size implies existence of a smooth solution to the time-dependent Navier–Stokes equations (abstract)
  • 18 February 2021 – 11h00 to 12h00: Roland Maier :  Multiscale scattering in nonlinear Kerr-type media (abstract)
  • 10 December 2020 – 16h00 to 17h00: Ani Miraçi : A-posteriori-steered and adaptive p-robust multigrid solvers (abstract)
  • 9 December 2020 – 16h00 to 17h00: Riccardo Milani : Compatible Discrete Operator schemes for the unsteady incompressible Navier–Stokes equations (abstract)
  • 26 November 2020 – 16h00 to 17h00: Koondanibha Mitra : A posteriori error bounds for the Richards equation (abstract)
  • 19 November 2020 – 11h00 to 12h00: Joëlle Ferzly : Semismooth and smoothing Newton methods for nonlinear systems with complementarity constraints: adaptivity and inexact resolution (abstract)
  • 5 November 2020 – 11h00 to 12h00: Zhaonan Dong : On a posteriori error estimates for non-conforming Galerkin methods (abstract)
  • 22 October 2020 – 11h00 to 12h00: Théophile Chaumont-Frelet : A posteriori error estimates for Maxwell’s equations based on flux quasi-equilibration (abstract)
  • 15 October 2020 – 11h00 to 12h00: Florent Hédin : A hybrid high-order (HHO) method with non-matching meshes in discrete fracture networks (abstract)

2019 – 2020

  • 16 March 2020 – 15h00 to 16h00: Bochra Mejri : Topological sensitivity analysis for identification of voids under Navier’s boundary conditions in linear elasticity (abstract)
  • 25 February 2020 – 15h00 to 16h00: Jakub Both : Robust iterative solvers for thermo-poro-visco-elasticity via gradient flows (abstract)
  • 16 October 2019 – 14h00 to 15h00: Nicolas Pignet : Hybrid High-Order method for nonlinear solid mechanics (abstract)
  • 27 September 2019 – 15h00 to 16h00: Ivan Yotov : A nonlinear Stokes-Biot model for the interaction of a non-Newtonian fluid with poroelastic media (abstract)
  • 5 September 2019 – 15h00 to 16h00: Koondi Mitra : A fast and stable linear iterative scheme for nonlinear parabolic problems (abstract)

2018 – 2019

  • 11 July 2019 – 11h00 to 12h00: Jose Fonseca : Towards scalable parallel adaptive simulations with ParFlow (abstract)
  • 6 June 2019 – 11h00 to 12h00: Quanling Deng : High-order generalized-alpha methods and splitting schemes (abstract)
  • 12 April 2019 – 14h30 to 15h30: Menel Rahrah : Mathematical modelling of fast, high volume infiltration in poroelastic media using finite elements (abstract)
  • 18 March 2019 – 14h to 15h: Patrik Daniel : Adaptive hp-finite elements with guaranteed error contraction and inexact multilevel solvers (abstract)
  • 14 February 2019 – 15h to 16h: Thibault Faney, Soleiman Yousef : Accélération d’un simulateur d’équilibres thermodynamiques par apprentissage automatique (abstract)
  • 7 February 2019 – 11h to 12h: Gregor Gantner : Optimal adaptivity for isogeometric finite and boundary element methods (abstract)
  • 31 January 2019 – 14h30 to 15h30: Camilla Fiorini : Sensitivity analysis for hyperbolic PDEs systems with discontinuous solution: the case of the Euler Equations. (abstract)
  • 9 January 2019 – 11h to 12h: Zhaonan Dong : hp-Version Discontinuous Galerkin Methods on Polygonal and Polyhedral Meshes (abstract)
  • 13 December 2018 – 11h to 12h: Maxime Breden : An introduction to a posteriori validation techniques, illustrated on the Navier-Stokes equations (abstract)
  • 5 December 2018 – 11h00 to 12h00: Amina Benaceur : Model reduction for nonlinear thermics and mechanics (abstract)

2017 – 2018

  • 16 April 2018 – 15h to 16h: Simon Lemaire : An optimization-based method for the numerical approximation of sign-changing PDEs (abstract)
  • 20 Febraury 2018 – 15h to 16h: Thirupathi Gudi : An energy space based approach for the finite element approximation of the Dirichlet boundary control problem (abstract)
  • 15 Febraury 2018 – 14h to 15h: Franz Chouly : About some a posteriori error estimates for small strain elasticity (abstract)
  • 30 November 2017 – 14h to 15h: Sébastien Furic : Construction & Simulation of System-Level Physical Models (abstract)
  • 2 November 2017 – 11h to 12h: Hend Benameur: Identification of parameters, fractures ans wells in porous media (abstract)
  • 10 October 2017 – 11h to 12h: Peter Minev: Recent splitting schemes for the incompressible Navier-Stokes equations (abstract)
  • 18 September 2017 – 13h to 14h: Théophile Chaumont: High order finite element methods for the Helmholtz equation in highly heterogeneous media (abstract)

2016 – 2017

  • 29 June 2017 – 15h to 16h: Gouranga Mallik: A priori and a posteriori error control for the von Karman equations (abstract)
  • 22 June 2017 – 15h to 16h: Valentine Rey: Goal-oriented error control within non-overlapping domain decomposition methods to solve elliptic problems (abstract)
  • 15 June 2017 – 15h to 16h:
  • 6 June 2017 – 11h to 12h: Ivan Yotov: Coupled multipoint flux and multipoint stress mixed finite element methods for poroelasticity (abstract)
  • 1 June 2017 – 10h to 12h:
    • Joscha Gedicke: An adaptive finite element method for two-dimensional Maxwell’s equations (abstract)
    • Martin Eigel: Adaptive stochastic FE for explicit Bayesian inversion with hierarchical tensor representations (abstract)
    • Quang Duc Bui: Coupled Parareal-Schwarz Waveform relaxation method for advection reaction diffusion equation in one dimension (abstract)
  • 16 May 2017 – 15h to 16h: Quanling Deng: Dispersion Optimized Quadratures for Isogeometric Analysis (abstract)
  • 11 May 2017 – 15h to 16h: Sarah Ali Hassan: A posteriori error estimates and stopping criteria for solvers using domain decomposition methods and with local time stepping (abstract)
  • 13 Apr. 2017 – 15h to 16h: Janelle Hammond: A non intrusive reduced basis data assimilation method and its application to outdoor air quality models (abstract)
  • 30 Mar. 2017 – 10h to 11h: Mohammad Zakerzadeh: Analysis of space-time discontinuous Galerkin scheme for hyperbolic and viscous conservation laws (abstract)
  • 23 Mar. 2017 – 15h to 16h: Karol Cascavita: Discontinuous Skeletal methods for yield fluids (abstract)
  • 16 Mar. 2017 – 15h to 16h: Thomas Boiveau: Approximation of parabolic equations by space-time tensor methods (abstract)
  • 9 Mar. 2017 – 15h to 16h: Ludovic Chamoin: Multiscale computations with MsFEM: a posteriori error estimation, adaptive strategy, and coupling with model reduction (abstract)
  • 2 Mar. 2017 – 15h to 16h: Matteo Cicuttin: Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming. (abstract)
  • 23 Feb. 2017
    – 10h to 10h45 : Lars Diening: Linearization of the p-Poisson equation (abstract)
    – 10h45 to 11h30 : Christian Kreuzer: Quasi-optimality of discontinuous Galerkin methods for parabolic problems (abstract)
  • 26 Jan. 2017 – 15h to 16h: Amina Benaceur:  An improved reduced basis method for non-linear heat transfer (abstract)
  • 19 Jan. 2017 – 15h to 16h: Laurent Monasse: A 3D conservative coupling between a compressible flow and a fragmenting structure (abstract)
  • 5 Jan. 2017 – 15h to 16h: Agnieszka Miedlar: Moving eigenvalues and eigenvectors by simple perturbations (abstract)
  • 8 Dec. 2016 – 15h to 16h: Luca Formaggia: Hybrid dimensional Darcy flow in fractured porous media, some recent results on mimetic discretization (abstract)
  • 22 Sept. 2016 – 15h to 16h: Paola Antonietti: Fast solution techniques for high order Discontinuous Galerkin methods (abstract)

2015 – 2016

  • 29 Oct. 2015 – 15h to 16h: Sarah Ali Hassan: A posteriori error estimates for domain decomposition methods (abstract)
  • 05 Nov. 2015 – 16h to 17h: Iain Smears: Robust and efficient preconditioners for the discontinuous Galerkin time-stepping method (abstract)
  • 12 Nov. 2015 -16h to 17h: Elyes Ahmed: Space-time domain decomposition method for two-phase flow equations (abstract)
  • 19 Nov. 2015 – 16h to 17h: Géraldine Pichot: Generation algorithms of stationary Gaussian random fields (abstract)
  • 26 Nov. 2015-16h to 17h: Jérôme Jaffré:  Discrete reduced models for flow in porous media with fractures and barriers (abstract)
  • 03 Dec. 2015 – 16h to 17h: François Clément: Safe and Correct Programming for Scientific Computing (abstract)
  • 10 Dec. 2015 – 16h to 17h: Nabil Birgle: Composite Method on Polygonal Meshes (abstract)11 Feb. 2016: Michel
  • Kern: Reactive transport in porous media: Formulations and numerical methods
  • 25 Feb. 2016: Martin Vohralík
  • 3 March 2016: François Clément: Safe and Correct Programming for Scientific Computing pt II

Analysis of spurious oscillations problem of Finite Volume Methods for low Mach number flows in fluid mechanics

Ibtissem Lannabi: Thursday, 23rd January 2025 at 11:00 This work is devoted to the numerical simulation of low Mach number flows, modeled by the compressible Euler system. Commonly used solvers for discretizing this model are Godunov-type schemes. These schemes exhibit poor performance at low Mach number in terms of efficiency and accuracy.Indeed, when the Mach number tends to zero, material and acoustic waves propagate on two distinct time scales, making temporal discretization challenging.In particular, an explicit scheme is stable under a CFL condition, which depends on the speed of sound, making this criterion very restrictive.Regarding the accuracy problem observed with quadrangular grids, it arises from the fact that the discrete solution fails to converge to the incompressible solution as the Mach number tends to zero.To overcome this accuracy problem, many fixes have been developed and consist in modifying the numerical diffusion of the original scheme. These corrections improve the accuracy of compressible schemes as the Mach number goes to zero. Unfortunately they introduce other problems, such as the appearance of numerical oscillations (checkerboard modes on a Cartesian grid) in the numerical solution, or the damping of acoustic waves as the Mach number goes to zero. Efficiency is also compromised as these schemes are stable under a more restrictive CFL condition compared to the original scheme. In this talk, we propose to study the phenomenon of oscillations that plagues some of the fixes proposed in the literature. We focus on Roe-type fixes, in particular those that reduce the numerical diffusion on the jump of the normal velocity.The asymptotic analysis of these schemes leads to a discretization of a wave system in which the pressure gradient is centered. To better understand the phenomenon, we focus on the linear wave system.We then show that this fix is not TVD, unlike the Godunov scheme,…

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Iterative solvers and optimal complexity of adaptive finite element methods

Ani Miraci: Tuesday, 17th December at 11:00 Finite element methods (FEMs) are often used to discretize second-order elliptic partial differential equations (PDEs). While standard FEMs rely on underlying uniform meshes, adaptive FEMs (AFEMs) drive the local mesh-refinement to capture potential singularities of the (unknown) PDE solution (stemming, e.g., from the data or the domain geometry). Crucially, adaptivity is steered by reliable a posteriori error control, often encoded in the paradigm SOLVE — ESTIMATE — MARK — REFINE. AFEMs allow to obtain optimal rates of convergence with respect to the number of degrees of freedom (an improvement to standard FEMs). However, in terms of computational costs, an adaptive algorithm is inherently cumulative in nature: an initial coarse mesh is used as input and exact finite element solutions need to be computed on consecutively refined meshes before a desired accuracy can be ensured. Thus, in practice, one strives instead to achieve optimal complexity, i.e., optimal rate of convergence with respect to the overall computational cost. The core ingredient needed for optimal complexity consists in the use of appropriate iterative solvers to be integrated as the SOLVE module within the adaptive algorithm. More precisely, one requires:(i) a solver whose each iteration is: (a) of linear complexity and (b) contractive;(ii) a-posteriori-steered solver-stopping criterion which allows to discern and balance discretization and solver error;(iii) nested iteration, i.e., the last computed solver-iterate is used as initial guess in the newly-refined mesh. First, we develop an optimal local multigrid for the context of symmetric linear elliptic second order PDEs and a finite element discretization with a fixed polynomial degree p and a hierarchy of bisection-generated meshes with local size h. The solver contracts the algebraic error hp-robustly and comes with a built-in a posteriori estimator equivalent to the algebraic error.Second, the overall adaptive algorithm is then shown…

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A parameter-free HDG method for linear elasticity with strongly symmetric stress

Lina Zhao: Thursday, 12th December at 11:00 In this talk, we present a parameter-free hybridizable discontinuous Galerkin (HDG) method of arbitrary polynomial orders for the linear elasticity problem, where the symmetry of stress is strongly imposed. The $H(\tdiv;\Omega)$-conforming space is used for the approximation of the displacement and the standard polynomial space is used for the approximation of the stress. The tangential trace of displacement acts as the Lagrange multiplier. The quasi-optimal approximation (up to data-oscillation term) is established for the $L^2$-error of stress and discrete $H^1$-error of displacement with $\lambda$-independent constants without requiring additional regularity assumption.  To guide adaptive mesh refinement, $\lambda$-robust a posteriori error estimator is derived. Several numerical experiments will be reported to demonstrate the performance of the proposed scheme.

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𝐻² conforming virtual element discretization of nondivergence form elliptic equations

Guillaume Bonnet: Thursday, 21st November at 11:00 The numerical discretisation of elliptic equations in nondivergence form is notoriously challenging, due to the lack of a notion of weak solutions based on variational principles. In many cases, there still is a well-posed variational formulation for such equations, which has the particularity of being posed in 𝐻², and therefore leads to a strong solution. Galerkin discretizations based on this formulation have been studied in the literature. Since 𝐻² conforming finite elements tend to be considered impractical, most of these discretizations are of discontinuous Galerkin type. On the other hand, it has been observed in the virtual element literature that the virtual element method provides a practical way to build 𝐻² conforming discretizations of variational problems. In this talk, I will describe a virtual element discretization of equations in nondivergence form. I will start with a simple linear model problem, and show how the 𝐻² conformity of the method allows for a particularly simple well-posedness and error analysis. I will then discuss the extension to equations with lower-order terms and with Hamilton-Jacobi-Bellman type nonlinearities, and present some numerical results.

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A view into the development of the FEniCS project over two decades

Jørgen S. Dokken: Thursday, 10th October at 11:00 The FEniCS project was started in 2003 as a collaboration between ToyotaTechnological Institute at Chicago, The University of Chicago and Chalmers University of Technology. The vision of the project was to create an open-source project that included the automation of modelling, optimization and discretization of differential equations. The plan was to create a generalized and efficient framework that was easy to use. With this goal the project expanded from being a pure C++ code (DOLFIN) to being a combined C++/Python framework for solving PDEs. One of the most notable outcomes of the project is the Unified Form Language, a domain specific language for representing PDEs in a variational form using computational symbolic algebra. In this talk, I will go through some of the historical context of the FEniCS project and its evolution into DOLFINx (DOI: 10.5281/zenodo.10447666). A presentation of the core components will highlight the newest developments and the extensibility of the framework.

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Robust augmented energy a posteriori estimates for Lipschitz and strongly monotone elliptic problems.

André Harnist: Tuesday, 15th October at 11:00 We design a posteriori estimates for finite element approximations of nonlinear elliptic problems satisfying strong-monotonicity and Lipschitz-continuity properties. These estimates include and build on, any iterative linearization method that satisfies a few clearly identified assumptions; this encompasses the Picard, Newton, and Zarantonello linearizations. The estimates give a guaranteed upper bound on an augmented energy difference (reliability with constant one), as well as a lower bound (efficiency up to a generic constant). We prove that for the Zarantonello linearization, this generic constant only depends on the space dimension, the mesh shape regularity, and possibly the approximation polynomial degree in four or more space dimensions, making the estimates robust with respect to the strength of the nonlinearity. For the other linearizations, there is only a computable dependence on the local variation of the linearization operators. We also derive similar estimates for the usual energy difference that depend locally on the nonlinearity and improve the established bound. Numerical experiments illustrate and validate the theoretical results, for both smooth and singular solutions.

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