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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

June 6 – Ivan Yotov: Coupled multipoint flux and multipoint stress mixed finite element methods for poroelasticity

Ivan Yotov: Tuesday 6 June at 11 am, A415 Inria Paris. We discuss mixed finite element approximations for the Biot system of poroelasticity. We employ a weak stress symmetry elasticity formulation with three fields – stress, displacement, and rotation, as well as a mixed velocity-pressure Darcy formulation. The method is reduced to a cell-centered scheme for the displacement and the pressure, using the multipoint flux mixed finite element method for flow and the recently developed multipoint stress mixed finite element method for elasticity. The methods utilize the Brezzi-Douglas-Marini spaces for velocity and stress and a trapezoidal-type quadrature rule for integrals involving velocity, stress, and rotation, which allows for local flux, stress, and rotation elimination. We perform stability and error analysis and present numerical experiments illustrating the convergence of the method and its performance for modeling flows in deformable reservoirs. This is joint work with Ilona Ambartsumyan and Eldar Khattatov, University of Pittsburgh.

April 13 – Jannelle Hammond: A non intrusive reduced basis data assimilation method and its application to outdoor air quality models

Jannelle Hammond: Thursday 13 April at 15 pm, A315 Inria Paris. With increased pollutant emissions and exposure due to mass urbanization worldwide, air quality measurement campaigns and epidemiology studies on air pollution and health effects have become increasingly common to estimate individual exposures and evaluate their association to various illnesses. As air pollution concentrations are known to be highly heterogeneous, sophisticated physically based air quality models (AQMs), in particular CFD based models, can provide spatially rich approximations and enable to better estimate individual exposure. In this work we investigate reduced basis (RB) methods [1] to diminish the resolution cost of advanced AQMs developed for concentration evaluation at urban scales. These models depend on varying parameters including meteorological conditions and pollutant emissions, often unknown at the micro scale. RB methods use approximation spaces made of suitable samples of solutions of AQMs governed by parameterized partial differential equations (PDEs), to rapidly construct accurate and computationally efficient approximations. A key to this technique is decomposing computational work into an offline and online stage. The RB functions used to build approximation spaces and all expensive parameter-independent terms, are computed “offline” once and stored, whereas inexpensive parameter-dependent quantities are evaluated “online “ for each new value of the parameters. However, the decomposition of the matrices into offline-online pieces requires modifying the calculation code, an intrusive procedure, which in some situations is impractical. In this work, we extend the Parameterized-Background Data-Weak (PBDW) method introduced in [2] to physically based AQMs. We will generate a sample of solutions from physical AQMs with varying meteorological conditions and pollution emissionsto build the RB approximation space and combine it with experimental observations, using the method in [3], to improve pollutant concentration estimations, with the goal of collaboration with an epidemiology exposure assessment team at the University of California-Berkeley. The goal…

March 30th – Mohammad Zakerzadeh: Analysis of space-time discontinuous Galerkin scheme for hyperbolic and viscous conservation laws

Mohammad Zakerzadeh: Thursday 30 March at 10 am, A415 Inria Paris. The well-posedness of the entropy weak solutions for scalar conservation laws is a classical result. However, for multidimensional hyperbolic systems, some theoretical and numerical evidence cast doubt on that entropy solutions constitute the appropriate solution paradigm, and it has been conjectured that the more general EMV solutions ought to be considered the appropriate notion of solution. In the numerical framework and building on previous results, we prove that bounded solutions of a certain class of space-time discontinuous Galerkin (DG) schemes converge to an EMV solution. The novelty in our work is that no streamline-diffusion (SD) terms are used for stabilization. While SD stabilization is often included in the analysis of DG schemes, it is not commonly found in practical implementations. We show that a properly chosen nonlinear shock-capturing operator success to provide the necessary stability and entropy consistency estimates. In case of scalar equations this result can be strengthened and the reduction to the entropy weak solution is obtained. We prove the boundedness of the solutions as well as the consistency with all entropy inequalities, and consequently the convergence to the entropy weak solution is obtained. For viscous conservation laws, we extend our framework to general convection-diffusion systems, with both nonlinear convection and nonlinear diffusion, such that the entropy stability of the scheme is preserved. It is well-known that this property is not guaranteed, even if the convective discretization is entropy stable with respect to the purely hyperbolic problem with a naive formulation of the viscous fluxes. We use a mixed formulation, and handle the difficulties arising from the nonlinearity of the viscous flux by an additional Galerkin projection operator. We prove the entropy stability of the method for different treatments of the viscous flux, thus unifying and extending…

March 23rd – Karol Cascavita: Discontinuous Skeletal methods for yield fluids

Karol Cascavita: Thursday 23 March at 3 pm, A415 Inria Paris. Bingham fluids model are a group of non-Newtonian fluids with a wide and diverse range of applications in industry and research. These materials are governed by a yield limit stress, which determines solid- or fluid-like features. This behavior is model by a viscoplastic term that introduces a non-linearity in the constitutive equations. Hence, the great difficulty to solve the problem, due to the non-regularity along with the a priori unknown solid-fluid boundaries. The yield stress model considered is the Bingham model, which despite being the simplest viscoplastic model is still considered a hot problem to solve theoretically and experimentally. The approaches proposed to handle this difficulties are mainly regularization methods and augmented Lagrangian algorithms. The first technique adds a regularization parameter to smooth the problem avoiding the singularity in the rigid zones. This procedure permits an straightforward implementation at the expense of a deterioration on the accuracy. The remaining technique solves the variational problem by uncoupling nonlinearities and the gradients. All the above methods are mainly approximating solutions in a finite-element or a finite volume framework. In this work, we focus on a different discretization technique named the Discontinuous Skeletal method, introduced recently by Di Pietro et al. The aim of this work is to perform an h-adaptation to enhance the prediction of the solid-liquid boundary, exploding the salient features of the DISK method. For instance: supports general meshes, face and cell-based unknowns formulation, high-order reconstruction operator, locally conservative.

March 16th – Thomas Boiveau: Approximation of parabolic equations by space-time tensor methods

Thomas Boiveau: Thursday 16 March at 3 pm, A415 Inria Paris. Abstract: In numerical simulations, the reduction of computational costs is a key challenge for the development of new models and algorithms; tensor methods are widely used for this purpose. In this work, we consider parabolic equations and define a mathematical framework in order to use iterative low-rank greedy algorithms, based on the separation of the space and time variables. The problem is handled using a minimal residual formulation. We perform numerical tests to compare the proposed method with the strategies already suggested in the literature.

March 2nd – Matteo Cicuttin: Implementation of Discontinuous Skeletal methods on arbitrary-dimensional, polytopal meshes using generic programming.

Matteo Cicuttin: Thursday 2 March at 3 pm, A415 Inria Paris. Abstract: Discontinuous Skeletal methods are devised at the mathematical level in a dimension-independent and cell-shape-independent fashion. Their implementation, at least in principle, should conserve this feature: a single piece of code should be able to work in any space dimension and to deal with any cell shape. It is not common, however, to see software packages taking this approach. In the vast majority of the cases, the codes are capable to run only on few very specific kinds of mesh, or only in 1D or 2D or 3D. On the one hand, this can happen simply because a fully general tool is not always needed. On the other hand, the programming languages commonly used by the scientific computing community (in particular Fortran and Matlab) are not easily amenable to an implementation which is generic and efficient at the same time. The usual (and natural) approach, in conventional languages, is to have different versions of the code, for example one specialized for 1D, one for 2D and one for 3D applications, making the overall maintenance of the codes rather cumbersome. The same considerations generally apply to the handling of mesh cells with various shapes, i.e., codes written in conventional languages generally support only a limited (and set in advance) number of cell shapes. Generic programming offers a valuable tool to address the above issues: by writing the code generically, it is possible to avoid making any assumption neither on the dimension (1D, 2D, 3D) of the problem, nor on the kind of mesh. In some sense, writing generic code resembles writing pseudocode: the compiler will take care of giving the correct meaning to each basic operation. As a result, with generic programming there will be still differents versions of the…

February 23rd – Christian Kreuzer: Quasi-optimality of discontinuous Galerkin methods for parabolic problems

Christian Kreuzer: 23 February at 10h45 am, A415 Inria Paris. It is a well known fact that inf-sup stable Galerkin discretisations of linear continuous problem provide quasi-optimal approximations in the corresponding norms. For elliptic problems, this is e.g. known as Cea’s Lemma. A priori error bounds are then typically obtained with the help of some (quasi)-interpolation. We apply this principle to parabolic problems and prove inf-sup stability and thus quasi-optimality of space and time adaptive backward Euler-Galerkin discretisations. In a second step, we define a reasonable (quasi)-interpolation operator and conclude a priori error bounds. In 1982 Dupont presented a counter example showing non-convergence of the backward Euler-Galerkin in the presence of spatial mesh changes. In this case, our bound contains an additional term, which is consistent with Dupont’s observation.

February 23rd – Lars Diening: Linearization of the p-Poisson equation

Lars Diening: 23 February at 10 am, A415 Inria Paris. This is a joint work with Massimo Fornasier and Maximilian Wank. In this talk we propose a iterative method to solve the non-linear -Poisson equation. The method is derived from a relaxed energy by an alternating direction method. We are able to show algebraic convergence of the iterates to the solution. However, our numerical experiments based on finite elements indicate optimal, exponential convergence.

March 9th – Ludovic Chamoin: Simulations multiéchelles avec MsFEM: estimation d’erreur a posteriori, stratégie adaptative, et couplage avec la reduction de modèle

The Multiscale Finite Element Method (MsFEM) is a powerful numerical method in the context of multiscale analysis. It uses basis functions which encode details of the fine scale description, and performs in a two-stage procedure: (i) offline stage in which basis functions are computed solving local fine scale problems; (ii) online stage in which a cheap Galerkin approximation problem is solved using a coarse mesh. However, as in other numerical methods, a crucial issue is to certify that a prescribed accuracy is obtained for the numerical solution. In the present work, we propose an a posteriori error estimate for MsFEM using the concept of Constitutive Relation Error (CRE) based on dual analysis. It enables to effectively address global or goal-oriented error estimation, to assess the various error sources, and to drive robust adaptive algorithms. We also investigate the additional use of model reduction inside the MsFEM strategy in order to further decrease numerical costs. We particularly focus on the use of the Proper Generalized Decomposition (PGD) for the computation of multiscale basis functions. PGD is a suitable tool that enables to explicitly take into account variations in geometry, material coefficients, or boundary conditions. In many configurations, it can thus be efficiently employed to solve with low computing cost the various local fine-scale problems associated with MsFEM. In addition to showing performances of the coupling between PGD and MsFEM, we introduce dedicated estimates on PGD model reduction error, and use these to certify the quality of the overall MsFEM solution.

January 26th – Amina Benaceur: An improved reduced basis method for non-linear heat transfer

Amina Benaceur: January 26 at 3pm, A415 Inria Paris. We address the reduced order modeling of parameterized transient non-linear and non-affine partial differential equations (PDEs). In practice, both the treatment of non-affine terms and non-linearities result in an empirical interpolation method (EIM) that may not be affordable although it is performed `offline’, since it requires to compute various nonlinear trajectories using the full order model. An alternative to the EIM that lessens its cost for steady non-linear problems has been recently proposed by Daversion and Prudhomme so as to alleviate the global cost of the `offline’ stage in the reduced basis method (RBM) by enriching progressively the EIM using the computed reduced basis functions. In the present work, we adapt the latter ideas to transient PDEs so as to propose an algorithm that solely requires as many full-model computations as the number of functions that span both the reduced basis and the EIM spaces. The computational cost of the procedure can therefore be substantially reduced compared to the standard strategy. Finally, we discuss possible variants of the present approach.

Internal Seminar