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Internal Seminar

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:
- Jad Dabaghi: Adaptive inexact semi-smooth Newton methods for a contact between two membranes (abstract)
- Patrik Daniel: An adaptive hp-refinement strategy with computable guaranteed error reduction factors (abstract)
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

21th September – Alexandre IMPERIALE: Numerical methods for time domain wave propagation problems applied to ultrasonic testing modelling

Alexandre IMPERIALE Wednesday 21th Sep at 15:00 ABSTRACT: The Department of Imaging and Simulation for Control (DISC) at CEA – LIST is dedicated to developing Non-Destructive Testing (NDT) methods in advanced industrial contexts (e.g. nuclear energy, aeronautic, or petrochemical industries). Amongst different testing modalities, Ultrasonic Testing (UT) is widespread and plays a major role in numerous industrial processes. It relies on the propagation of mechanical waves in order to probe critical specimens, often formed with complex media – in terms of geometry or material properties. To fully understand the capabilities and performances of UT experiments, the DISC is developing modelling tools for wave propagation, which are bound to incorporate the CIVA platform [1] – a commercial software dedicated to NDT modelling. When commercializing modelling tools, efficiency and robustness are key features. This talk focuses on numerical methods for wave propagation problems that address these challenges. In particular, we show how the combination of Spectral Finite Elements [2] with the Mortar Element method [3] – a domain decomposition approach – can be tuned to render efficient and robust algorithms [4]. Coupled with high-frequency asymptotic methods [5] (e.g. ray-based algorithms), this combination forms the basis of various advances in the CIVA platform. This approach is typically used to modelling UT experiments relying on bulk wave propagation, e.g. for testing welds (typical nuclear energy industry applications) or composite materials [6] (typical aeronautic industry applications). Additionally, we present some details on ongoing works related to other UT configurations, such as numerical modelling of wave propagation through thin layers – based on effective transmission conditions – or within plate-like geometries – achieved through dedicated time schemes. [1] http://www.extende.com/civa-in-a-few-words [2] Cohen, G. C. “Higher-order numerical methods for transient wave equations”. Berlin: Springer, 2002 Vol. 5. [3] F. Ben Belgacem, Y. Maday, “The mortar element method…

13th June – Jean-Luc Guermond: Invariant-domain preserving IMEX time stepping methods

Jean-Luc Guermond Thursday 13th June at 11:00 ABSTRACT: I will present high-order time discretizations of a Cauchy problem where the evolution operator comprises a hyperbolic part and a parabolic part (say diffusion and stiff relaxation terms). The said problem is assumed to possess an invariant domain. I will propose a technique that makes every implicit-explicit (IMEX) time stepping scheme invariant domain preserving and mass conservative. The IMEX scheme is written in incremental form and, at each stage of the scheme, we first compute low-order hyperbolic and parabolic updates, followed by their high-order counterparts. The proposed technique, which is agnostic to the space discretization, allows to optimize the time step restrictions induced by the hyperbolic sub-step. To illustrate the proposed methodology, we derive three novel IMEX schemes with optimal efficiency and for which the implicit scheme is singly-diagonal and L-stable: a third-order, four-stage scheme; and two fourth-order schemes, one with five stages and one with six stages. The novel IMEX schemes are evaluated numerically on a stiff ODE system. We also apply these schemes to nonlinear convection-diffusion problems with stiff reaction and to compressible viscous flows possibly including grey radiation.

16th June – ‪Chérif Amrouche: Elliptic Problems in Lipschitz and in $C^{1,1}$ Domains

Chérif Amrouche Thursday 16th June at 11:30 ABSTRACT: We are interested here in questions related to the maximal regularity of solutions to elliptic problems with Dirichlet or Neumann boundary conditions (see ([1]). For the last 40 years, many works have been concerned with questions when Ω is a Lipschitz domain. Some of them contain incorrect results that are corrected in the present work. We give here new proofs and some complements for the case of the Laplacian (see [3]), the Bilaplacian ([2] and [6]) and the operator div (A∇) (see ([5]) when A is a matrix or a function. And we extend this study to obtain other regularity results for domains having an adequate regularity. We give also new results for the Dirichlet-to-Neumann operator for Laplacian and Bilaplacian. Using the duality method, we can then revisit the work of Lions-Magenes [4], concerning the so-called very weak solutions, when the data are less regular. References : [1] C. Amrouche and M. Moussaoui. Laplace equation in smooth or non smooth do- mains. Work in Progress. [2] B.E.J. Dahlberg, C.E. Kenig, J. Pipher and G.C. Verchota. Area integral estimates for higher-order elliptic equations and systems. Ann. Inst. Fourier, 47-5, 1425– 1461, (1997). [3] D. Jerison and C.E. Kenig. The Inhomogeneous Dirichlet Problem in Lipschitz Domains, J. Funct. Anal. 130, 161–219, (1995). [4] J.L. Lions and E. Magenes. Probl`emes aux limites non-homog`enes et applications, Vol. 1, Dunod, Paris, (1969). [5] J. Necas. Direct methods in the theory of elliptic equations. Springer Monographs in Mathematics. Springer, Heidelberg, (2012). [6] G.C. Verchota. The biharmonic Neumann problem in Lipschitz domains. Acta Math. 194-2, 217–279, (2005).

5th May – ‪Daniel Zegarra Vasquez: Simulation of single-phase flows in fractured porous media using the mixed hybrid finite element method

Daniel Zegarra Vasquez Thursday 5th May at 11:00 ABSTRACT: In underground environments, fractures are very numerous and present at all scales, with very heterogeneous sizes. In particular for flows, they are preferential channels: flows are much faster there than in the neighboring rock. Indeed, the permeability of rock is generally about two orders of magnitude lower than that of fractures. This makes fractures play a vital role in a large number of industrial and environmental applications. These particularities of the fractured porous domain make the modeling and simulation of the flows passing through it a major challenge today for which it is necessary to develop dedicated, robust and efficient models and numerical methods. The most commonly used model for representing fractures is the discrete fracture network (DFN) in which fractures are represented as structures of codimension 1. The model of single-phase flows in fractured porous media is described in [5]. The particularity of the fractured porous problem, compared to the porous-only or fractured-only problem [3], is the coupling between the flow in the fractures and the flow in the rock. Due to the difficulties encountered in taking into account the geometric complexity of large fractured networks in simulations, the test cases recently proposed in the literature are mainly 2D, or 3D with a limited number (about ten) of fractures [1]. In this talk, we will present the nef-flow-fpm solver, which solves the stationary 3D fractured porous problem using the mixed hybrid finite element method. The method developed in the solver is inspired by [4]. To mesh the domain, a first simplical and conforming 2D mesh is generated for the DFN and for the boundaries of the domain, then a second simplical and conforming 3D mesh is generated from the first mesh. The solvers integrated in nef-flow-fpm are direct solvers,…

7th April – ‪Christoph Lehrenfeld: Embedded Trefftz Discontinuous Galerkin methods

Christoph Lehrenfeld Thursday 7th April at 11:00 ABSTRACT: Discontinuous Galerkin (DG) methods are widely used to discretize partial differential equations (PDEs) due to (a.o.) flexibility for designing robust methods and simplicity in terms of data structures. One major drawback of DG methods is, however, the increased number of (globally coupled) degrees of freedom (ndof) compared to, for instance, continuous Galerkin methods. One – by now established – remedy is the use of Hybrid DG methods. These allow reducing the globally coupled ndof essentially by introducing the concept of static condensation for DG methods. Thereby the dimensions of global linear systems that need to be solved for reduced from O(p^d) to O(p^{d−1}), where d is the space dimension and p is the polynomial degree of the finite element space. A different approach is the use of Trefftz DG methods, where a DG formulation is modified by restricting the finite element spaces to functions that element-wise solve the PDE at hand. This results in a similar reduction of globally coupled ndof, cf. Figure 1 below. However, due to several limitations, Trefftz DG methods have only been applied for special PDEs so far. On the one hand, the finite element spaces have to be specifically tailored for each PDE type, on the other hand, inhomogeneous equations and non-constant coefficients in the differential operators are difficult to deal with and rarely treated. In this talk, we introduce Embedded Trefftz DG methods which exploit the existence of an underlying standard DG formulation for an efficient and flexible implementation of Trefftz DG methods. Furthermore, we relax Trefftz DG methods in view of the constraints on the finite element space leading to weak Trefftz DG spaces. Both together allow us to remove the limitations of Trefftz DG methods in order to enable them for a large…

19th April – ‪Christos Xenophontos: Finite Element approximation of singularly perturbed eigenvalue problems

Christos Xenophontos Tuesday 19th April at 14:00 ABSTRACT: We consider singularly perturbed eigenvalue problems in one-dimension, and their numerical approximation by the (standard Galerkin) Finite Element Method (FEM). These are fourth order equations, where a small parameter multiplies the highest order derivative. We will present results for an $h$ version FEM with polynomials of degree $p$ on an exponentially graded (eXp) mesh, as well as an $hp$ version FEM on the so-called Spectral Boundary Layer (SBL) mesh. For both methods, robust optimal convergence is shown for the eigenvalues and associated eigenfunctions. Numerical results, illustrating the theory, will also be presented. This is joint work with H. G. Roos.

24th March – ‪Miloslav Vlasak: A posteriori error estimates for discontinuous Galerkin method

Miloslav Vlasak Thursday 24th March at 11:00 ABSTRACT: We will present a posteriori error estimate for higher-order time discretizations, most importantly for the discontinuous Galerkin method, cf. [1]. Rather than the presentation of the estimates themselves, the talk shall focus on the most important ideas behind and their possible application to spatial nonconforming discretizations, most importantly to the discontinuous Galerkin method again. Overall, the talk shall rather focus on open problems than on the presentation of the fully completed results. Additionally, the ideas of reconstructions by the Radau polynomials that are the core ideas in a posteriori error estimates for time discretizations can be exploited for the direct efficiency analysis of the derived estimates. This can enable tracking the dependence of the efficiency constant on the discretization polynomial degree in 1D, cf. [2]. Possible extensions of this result to multiple dimensions shall be discussed. References [1] V. Dolejsi, F. Roskovec, M. Vlasak: A posteriori error estimates for higher order space-time Galerkin discretizations of nonlinear parabolic problems, SIAM J. Numer. Anal. 59, N. 3, 1486–1509 (2021) [2] M. Vlasak: On polynomial robustness of flux reconstructions, Appl. Math. 65, N. 2, 153–172 (2020)

14th April – ‪Idrissa Niakh: Stable model reduction for linear variational inequalities with parameter-dependent constraints

‪Idrissa Niakh Thursday 14th April at 11:00 ABSTRACT: We consider model reduction for linear variational inequalities with parameter-dependent constraints. We study the stability of the reduced problem in the context of a dualized formulation of the constraints using Lagrange multipliers. Our main result is an algorithm that guarantees inf-sup stability of the reduced problem. The algorithm is computationally effective since it can be performed in the offline phase even for parameter-dependent constraints. Moreover, we also propose a modification of the Cone Projected Greedy algorithm so as to avoid ill-conditioning issues when manipulating the reduced dual basis. Our results are illustrated numerically on the frictionless Hertz contact problem between two half-spheres with parameter-dependent radius and on the membrane obstacle problem with parameter-dependent obstacle geometry.

10th March – ‪Ruma Maity: Parameter dependent finite element analysis for ferronematics solutions

Ruma Maity‬‬ Thursday 10th March at 11:00 ABSTRACT: In this talk, we focus on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well, referred to as ferronematics. We discuss the asymptotic analysis of global energy minimizers in the limit of vanishing elastic constant, where the re-scaled elastic constant l is inversely proportional to the domain area. The conforming finite element method is used to approximate the regular solutions of the corresponding non-linear system of partial differential equations with cubic nonlinearity and non-homogeneous Dirichlet boundary conditions. We establish the existence and local uniqueness of the discrete solutions, error estimates in the energy and L2 norms with l- discretization parameter dependency. The theoretical results are complemented by the numerical experiments on the discrete solution profiles, and the numerical convergence rates that corroborate the theoretical estimates. This talk is based on joint works with Apala Majumdar (Department of Mathematics and Statistics, University of Strathclyde, UK) and Neela Nataraj (Department of Mathematics, Indian Institute of Technology Bombay, India).

27th January – ‪Frédéric Lebon‬‬ : On the modeling of nonlinear imperfect solid/solid interfaces by asymptotic techniques

Frédéric Lebon‬‬ Thursday 27th January at 11:00 ABSTRACT: In this talk, we will focus on the theoretical and numerical modelling of interfaces between solids (adhesion, bonding, friction, etc.). We will present a general methodology based on matched asymptotic theory to obtain families of models including the relative rigidity of the interphase (soft or hard), geometrical or material non-linearities (plasticity, curvature, finite strain, …), damage and multiphysics couplings (thermics, piezoelectricity, …). Numerical results will be presented.

Internal Seminar