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Internal Seminar Calendar

2024 – 2025

  • 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

A Volume-Preserving Reference Map Method for the Level Set Representation

Maxime Theillard： Thursday 16th Nov at 17:00 Abstract: This seminar will present an implicit interface representation, where the geometry is captured by a level set function, and its deformations are reconstructed from the diffeomorphism between the warped and original geometries (the reference map). A key advantage of this representation is that it provides a local estimation of numerical local mass losses. Using this metric, we design a novel projection for the reference map on the space of volume- preserving diffeomorphisms, which results in enhanced but inexact, mass conservation. In the limit of small deviations from this space, the projection is shown to be uniquely defined, and the correction can be computed as the solution of a Poisson problem. The method is analyzed and validated in two and three spatial dimensions. Both the theoretical and computational results show it excels at correcting the mass loss due to inaccuracy in the advection process or the velocity field. This error reduction is particularly impactful for practical applications, such as the simulation of multiphase flows over long time intervals, and offers improved computational exploration capabilities.

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Computer-assisted proofs for nonlinear equations: how to turn a numerical simulation into a theorem.

Maxime Breden: Thursday 9th Nov at 11:00am Abstract: The goal of a posteriori validation methods is to get a quantitative and rigorous description of some specific solutions of nonlinear dynamical sys- tems, often ODEs or PDEs, based on numerical simulations. The general strategy consists in combining a priori and a posteriori error estimates, in- terval arithmetic, and a fixed point theorem applied to a quasi-Newton op- erator. Starting from a numerically computed approximate solution, one can then prove the existence of a true solution in a small and explicit neigh- borhood of the numerical approximation. I will first present the main ideas behind these techniques on a simple example, and then describe the results of a recent joint work with Jan Bouwe van den Berg and Ray Sheombarsing, in which we use these techniques to rigorously enclose solutions of some parabolic PDEs.

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Implementing $H^2$-conforming finite elements without enforcing $C^1$-continuity

Charles Parker: Monday 13th Nov at 11:00am ABSTRACT: Fourth-order elliptic problems arise in a variety of applications from thin plates to phase separation to liquid crystals. A conforming Galerkin discretization requires a finite dimensional subspace of $H^2$, which in turn means that conforming finite element subspaces are $C^1$-continuous. In contrast to standard $H^1$-conforming $C^0$ elements, $C^1$ elements, particularly those of high order, are less understood from a theoretical perspective and are not implemented in many existing finite element codes. In this talk, we address the implementation of the elements. In particular, we present algorithms that compute $C^1$ finite element approximations to fourth-order elliptic problems and which only require elements with at most $C^0$-continuity. We show that the resulting subproblems are uniformly stable with respect to the mesh size and polynomial degree in 2D and illustrate the method on a number of representative test problems.

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A posteriori error estimates robust with respect to nonlinearities and final time.

Martin Vohralík: Thursday, 25th May at 11:00 ABSTRACT: A posteriori estimates enable us to certify the error committed in a numerical simulation. In particular, the equilibrated flux reconstruction technique yields a guaranteed error upper bound, where the flux obtained by local postprocessing is of independent interest since it is always locally conservative. In this talk, we tailor this methodology to model nonlinear and time-dependent problems to obtain estimates that are robust, i.e., of quality independent of the strength of the nonlinearities and the final time. These estimates include and build on common iterative linearization schemes such as Zarantonello, Picard, Newton, or M- and L-ones. We first consider steady problems and conceive two settings: we either augment the energy difference by the discretization error of the current linearization step, or we design iteration-dependent norms that feature weights given by the current iterate. We then turn to unsteady problems. Here we first consider the linear heat equation and finally move to the Richards one, which is doubly nonlinear and exhibits both parabolic–hyperbolic and parabolic–elliptic degeneracies. Robustness with respect to the final time and local efficiency in both time and space are addressed here. Numerical experiments illustrate the theoretical findings all along the presentation.

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On the preconditioned Newton’s method for Richards’ equation

Konstantin Brenner: Thursday, 11th May at 11:00 ABSTRACT: Richards’ equation is arguably the most popular hydrogeological flow model, which can be used to predict the underground water movement under both saturated and unsaturated conditions. However, despite its importance for hydrogeological applications, this equation is infamous for being difficult to solve numerically. Indeed, depending on the flow parameters, the resolution of the systems arising after the discretization may become an extremely challenging task, as the linearization schemes such as Picard or Newton’s methods may fail or exhibit unacceptably slow convergence. In this presentation, I will first give a brief overview of Richards’ equation both from the hydrogeological and mathematical perspectives. Then we will discuss the nonlinear preconditioning strategies that can be used to improve the performance of Newton’s method. In this regard, I will present some traditional techniques involving the primary variables substitution as well as some recent ones based on the nonlinear Jacobi or block Jacobi preconditioning. The later family of (block) Jacobi-Newton methods turn out to be a very attractive option as they allow for the global convergence analysis in the framework of the Monotone Newton Theorem.

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High order exponential fitting discretizations for convection diffusion problems

Ludmil Zikatanov: Thursday, 4th May at 11:00 ABSTRACT: We discuss discretizations for convection diffusion equations in arbitrary spatial dimensions. Targeted applications include the Nernst-Plank equations for transport of species in a charged media. We illustrate how such exponentially fitted methods are derived in any spatial dimension. A main step in proving error estimates is showing unisolvence for the quasi-polynomial spaces of differential forms defined as weighted spaces of differential forms with polynomial coefficients. We show that the unisolvent set of functionals for such spaces on a simplex in any spatial dimension is the same as the set of such functionals used for the polynomial spaces. We are able to prove our results without the use of Stokes’ Theorem, which is the standard tool in showing the unisolvence of functionals in polynomial spaces of differential forms. This is joint work with Shuonan Wu (Beijing University).

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23rd March – Marien-Lorenzo Hanot: Polytopal discretization of advanced differential complexes.

Marien-Lorenzo Hanot: Thursday, 23rd March at 11:00 ABSTRACT: We are interested in the discretization of advanced differential complexes. That is to say, complexes presenting higher regularity or additional algebraic constraints compared to the De Rham complex.This type of complex appears naturally in the discretization of many systems of differential equations. For example, the Stokes complex uses the same operators as the De Rham complex. Still, it requires an increased regularity, or the Div-Div complex appears in biharmonic equations and requires the use of fields with values in symmetric or traceless matrices. The principle of polytopal methods is to use discrete functions not belonging to a subset of the continuous functions but are composed of a collection of polynomials defined on objects of any dimension of the mesh (on edges, faces, cells…).This allows using very generic meshes, in our case composed of arbitrary contractible polytopes, while keeping the computability of discrete functions. The objective is to present the construction of a family of discrete 3-dimensional Div-Div complexes for arbitrary polynomial degrees. These complexes are consistent on polynomial functions, which is the basis for obtaining an optimal convergence of the schemes built on them. Moreover, they preserve the algebraic structure of the continuous complex, in the sense that the cohomology of the discrete complex is isomorphic to that of the continuous. .

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Parameter studies automation with Prune_rs

Simon Legrand: Thursday 2nd February at 11:00 ABSTRACT: While essential in most scientific fields, parameter studies can be tedious and error-prone if they are not led with proper tools. Prune_rs (Prune in Rust) is a tool/language aimed at easily describing complex parameter spaces and automatizing the execution of commands over each parameter combination. It also offers the user predefined patterns to store results and simplifies postprocessing. Prune_rs is an ongoing development process and we would be glad to discuss your suggestions to make it better!

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