# Internal Seminar

## 2020 – 2021

• 3 February 2022 – 11h00 to 12h00: Pierre Matalon:
• 27 January 2022 – 11h00 to 12h00: Frédéric Lebon:
• 20 January 2022 – 11h00 to 12h00: Isabelle Ramière:
• 13 January 2022 – 11h00 to 12h00: Koondanibha Mitra:
• 10 December 2021 – 11h00 to 12h00: Gregor GantnerApplications of a space-time first-order system least-squares formulation for parabolic PDEs.
• 25 November 2021 – 11h00 to 12h00: Pierre GosseletAsynchronous Global/Local coupling. (abstract)
• 24 November 2021 – 10h30 to 11h30: Grégory EtangsaleA primal hybridizable discontinuous Galerkin method for modelling flows in fractured porous media. (abstract)
• (Reschedule in the future): Jean-Charles Passieux:
• 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 GedickeAn adaptive finite element method for two-dimensional Maxwell’s equations (abstract)
• Martin EigelAdaptive 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 BenaceurAn 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 AntoniettiFast solution techniques for high order Discontinuous Galerkin methods (abstract)

## 2015 – 2016

• 29 Oct. 2015 – 15h to 16h: Sarah Ali HassanA posteriori error estimates for domain decomposition methods (abstract)
• 05 Nov. 2015 – 16h to 17h: Iain SmearsRobust 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 PichotGeneration algorithms of stationary Gaussian random fields (abstract)
• 26 Nov. 2015-16h to 17h: Jérôme JaffréDiscrete 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

## 25 November – Pierre Gosselet: Asynchronous Global/Local coupling

Pierre Gosselet: Thursday 25th November at 11:00   ABSTRACT: Non-intrusive global/local coupling can be seen as an exact iterative version of the submodeling (structural zoom) technique widely used by industry in their simulations. A global model, coarse but capable of identifying general trends in the structure, is locally patched by fine models with refined geometries, materials and meshes. The coupling is achieved by alternating Dirichlet resolutions on the patches and global resolutions with a well-chosen immersed Neumann condition. After the preliminary work of (Whitcomb, 1991), the method has been rediscovered by many authors. Our work starts with (Gendre et al., 2009). From a theoretical point of view, the method is related to the optimized Schwarz domain decomposition methods (Gosselet et al., 2018). It has been applied in many contexts (localized or generalized (visco)plasticity, stochastic calculations, cracking, damage, fatigue…). In the ANR project ADOM, we are working on the implementation of an asynchronous version of the method. The expected benefits of asynchronism (Magoulès et al., 2018; Glusa et al., 2020) are to reach the solution faster, to adapt to many computational hardware by being more resilient in case of poor load balancing, network latencies or even outages. During the presentation, I will show how to adapt the global/local coupling to asynchronism and will illustrate its performance on thermal and linear elasticity calculations. This work is realized with the support of National Research Agency, project [ANR-18-CE46-0008]. [1] Gendre, Lionel et al. (2009). “Non-intrusive and exact global/local techniques for structural problems with local plasticity”. In: Computational Mechanics 44.2, pp. 233–245. [2] Glusa, Christian et al. (2020). “Scalable Asynchronous Domain Decomposition Solvers”. In: SIAM Journal on Scientific Computing 42.6, pp. C384–C409. doi: 10.1137/19M1291303. [3] Gosselet, Pierre et al. (2018). “Non-invasive global-local coupling as a Schwarz domain decomposition method: acceleration and generalization”. In: Advanced Modeling and…

## 24 November – Grégory Etangsale: A primal hybridizable discontinuous Galerkin method for modelling flows in fractured porous media

Grégory Etangsale: Wednesday 24th November at 10:30   ABSTRACT: Modeling fluid flow in fractured porous media has received tremendous attention from engineering, geophysical, and other research fields over the past decades. We focus here on large fractures described individually in the porous medium, which act as preferential paths or barriers to the flow. Two different approaches are available from a computational aspect: The first one, and definitively the oldest, consists of meshing inside the fracture. In this case, the flow is governed by a single Darcy equation characterized by a large scale of variation of the permeability coefficient within the matrix region and the fracture, respectively. However, this description becomes quite challenging since it requires a considerable amount of memory storage, severely increasing the CPU time. A more recent approach differs by considering the fracture as an encapsulated object of lower dimension, i.e., (d − 1)-dimension. As a result, the flow process is now governed by distinctive equations in the matrix region and fractures, respectively. Thus, coupling conditions are added to close the problem. This mathematical description of the fractured porous media has been initially introduced by Martin et al. in [4] and is referred to as the Discrete Fracture-Matrix (DFM) model. The DFM description is particularly attractive since it significantly simplifies the meshing of fractures and allows the coupling of distinctive discretizations such as Discontinuous and Continuous Galerkin methods inside the bulk region and the fracture network, respectively. For instance, we refer the reader to the recent works of Antonietti et al. [1] (and references therein), where the authors coupled the Interior Penalty DG method with the (standard) H1-Conforming finite element method to solve the DFM problem (see e.g., [3]). However, it is well-known that DG methods are generally more expensive than most other numerical methods due to their high…

## EFEF 2021

https://efef2020.inria.fr/

## 06 September – Rolf Stenberg: Nitsche’s Method for Elastic Contact Problems

Rolf Stenberg: Monday 06th June at 15:00   ABSTRACT: In this talk, we present a priori and a posteriori error estimates for the frictionless contact problem between two elastic bodies. The analysis is built upon interpreting Nitsche’s method as a stabilised finite element method for which the error estimates can be derived with minimal regularity assumptions and without a saturation assumption. The stabilising term corresponds to a master-slave mortaring technique on the contact boundary. The numerical experiments show the robustness of Nitsche’s method and corroborate the efficiency of the a posteriori error estimators. [1] T. Gustafsson, R. Stenberg, J. Videman. On Nitsche’s method for elastic contact problems. SIAM Journal of Scientific Computing. 42 (2020) B425–B446 [2] T. Gustafsson, R. Stenberg, J. Videman. The masters-slave Nitsche method for elastic contact problems. Numerical Mathematics and Advanced Applications – ENUMATH 2019. J.F. Vermolen, C. Vuik, M. Moller (Eds.). Springer Lecture Notes in Computational Science and Engineering. 2021

## 17 June – Elyes Ahmed: Adaptive fully-implicit solvers and a posteriori error control for multiphase flow with wells

Elyes Ahmed: Thursday 17 June at 11:00 am   ABSTRACT: Flow is driven by the wells in most reservoir simulation workflows. From a numerical point of view,  wells can be seen as singular source-terms due to their small-scale relative to grid blocks used in field-scale simulation. Near-well models, such as Peaceman model, are used to account for the highly non-linear flow field in the vicinity of the wellbore. The singularities that wells introduce in the solution create difficulties for the gridding strategy and usually result in a less flexible time-stepping strategy to ensure convergence of the nonlinear solver. We present in this work a-posteriori error estimators for multiphase flow with singular well sources. The estimators are fully and locally computable and target the singular effects of wells.  The error estimate uses the appropriate weighted norms, where the weight weakens the norm only around the wells, letting it behave like the usual H^{1} -norm far from the near-well region. The error estimators are used to modify a fully implicit solver in the MATLAB Reservoir Simulation Toolbox (MRST). We demonstrate the benefits of the adaptive implicit solver through a range of test cases.

## 3 June – Oliver Sutton: High order, mesh-based multigroup discrete ordinates schemes for the linear Boltzmann transport problem.

Oliver Sutton: Thursday 3 June at 11:00 am   ABSTRACT: The linear Boltzmann problem is a widely used model for the transport of particles through a scattering medium, such as neutrons in a nuclear reactor, or photons during radiotherapy or in the atmosphere of a star. The key challenge in simulating such phenomena using this model lies in the fact that the problem is an integro-partial-differential equation in 6 independent variables: three position variables and three momentum variables (7 if time is also included). Despite this, there is a long history of this model being successfully applied in practice. A well-studied class of numerical schemes for simulating phenomena governed by this model couples a discontinuous Galerkin spatial discretisation with a multigroup discrete-ordinates discretisation in the momentum variables. Standard multigroup discrete ordinates discretisations may be viewed as employing a piecewise constant approximation space, and possess the particularly attractive characteristic of decoupling the fully-coupled problem into a sequence of three-dimensional linear transport problems which may be solved independently and in parallel. In this talk, we will discuss a new generalisation of these multigroup discrete ordinates schemes. These new schemes employ arbitrarily high order polynomials in the discretisation of the momentum variables, providing high order convergence properties, and offer a familiar Galerkin framework for their analysis. Crucially, moreover, they retain the simple algorithmic structure of their classical counterparts.

## 29 April – Lorenzo Mascotto: Enriched nonconforming virtual element methods

Lorenzo Mascotto: Thursday 29 April at 11:00 am ABSTRACT: Solutions to elliptic partial differential equations (PDEs) on smooth domains with smooth data are smooth. However, when solving a PDE on a Lipschitz polygon, its solution is singular at the vertices of the domain. The singular behaviour is known a priori: the solution can be split as a sum of a smooth term, plus series of singular terms that belong to the kernel of the differential operator appearing in the PDE. The virtual element method (VEM) is a generalization of the finite element method (FEM) to polygonal/polyhedral meshes and is based on approximation spaces consisting of solutions to local problems mimicking the target PDE and has been recently generalized to the extended VEM (XVEM). Here, the approximation spaces are enriched with suitable singular functions. A partition of unity (PU) is used to patch local spaces. The approach of the XVEM is close to that of the extended FEM. In this talk, we present a new paradigm for enriching virtual element (VE) spaces. Instead of adding special functions to the global space and eventually patch local spaces with a PU, we modify the definition of the local spaces by tuning the boundary conditions of local problems. By doing this, local VE spaces contain the desired singular functions, but there is no need to patch them with a PU. This results in an effective and slight modification of the already existing implementation of VE codes, as well as in a natural extension for existing theoretical results.

## 1 April – André Harnist: Improved error estimates for Hybrid High-Order discretizations of Leray–Lions problems

André Harnist: Thursday 1 April at 11:00 am Abstract: We consider Hybrid High-Order (HHO) approximations of Leray-Lions problems set in W^(1,p) with p in (1,2]. For this class of problems, negative powers of the gradient of the solution can appear in the flux. Depending on the expression of the latter, this can lead to a degeneracy of the problem when the gradient of the solution vanishes or becomes large. The goal of this presentation is to derive novel error estimates depending on the degeneracy of the problem inspired by [1,2,3]. Specifically, we show that, for the globally non-degenerate case, the energy-norm of the error has a convergence rate of (k+1), with k denoting the degree of the HHO approximation. In the globally degenerate case, on the other hand, the energy-norm of the error converges with a rate of (k+1)(p-1), coherently with the estimate originally proved in [4]. We additionally introduce, for each mesh element, a dimensionless number that captures the local degeneracy of the model and identifies the contribution of the element to the global error: from the fully degenerate regime, corresponding to a contribution in (k+1)(p-1), to the non-degenerate regime, corresponding to a contribution in (k+1), through all intermediate regimes. These regime-dependent error estimates are illustrated by a complete panel of numerical experiments. [1] M. Botti, D. Castanon Quiroz, D. A. Di Pietro and A. Harnist, A Hybrid High-Order method for creeping flows of non-Newtonian fluids, Submitted. 2020. URL: https://hal.archives-ouvertes.fr/hal-02519233. [2] D. A. Di Pietro and J. Droniou, The Hybrid High-Order Method for Polytopal Meshes. Modelling, Simulation and Application 19. Springer International Publishing, 2020. ISBN: 978-3-030-37202-6 (Hardcover) 978-3-030-37203-3 (eBook). DOI: 10.1007/978-3-030-37203-3. [3] D. A. Di Pietro and J. Droniou, A Hybrid High-Order method for Leray–Lions elliptic equations on general meshes, Math. Comp., volume 86, 2017, number 307, pages 2159–2191,…

## 11 March – Omar Duran: Explicit and implicit hybrid high-order methods for the wave equation in time regime

Omar Duran: Thursday 11 March at 15:00 There are two main approaches to derive a fully discrete method for solving the second-order acoustic wave equation in the time regime. One is to discretize directly the second-order time derivative and the Laplacian operator in space. The other approach is to transform the second-order equation into a first-order hyperbolic system. Firstly, we consider the time second-order form. We devise, analyze the energy-conservation properties, and evaluate numerically a hybrid high-order (HHO) scheme for the space discretization combined with a Newmark-like time-marching scheme. The HHO method uses as discrete unknowns cell- and face-based polynomials of some order 0 ≤ k, yielding for steady problems optimal convergence of order (k + 1) in the energy norm [1]. Secondly, inspired by ideas presented in [2] for hybridizable discontinuous Galerkin (HDG) method and the link between HDG and HHO methods in the steady case [3], first-order explicit or implicit time-marching schemes combined with the HHO method for space discretization are considered. We discuss the selection of the stabilization term and energy conservation and present numerical examples. Extension to the unfitted meshes is contemplated for the acoustic wave equation. We observe that the unfitted approach combined with local cell agglomeration leads to a comparable CFL condition as when using fitted meshes [4]. [1] D.A. Di Pietro, A. Ern, and S. Lemaire. An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators. Computational Methods in Applied Mathematics. 14 (2014) 461-472. [2] M. Stanglmeier, N.C. Nguyen, J. Peraire, and B. Cockburn. An explicit hybridizable discontinuous Galerkin method for the acoustic wave equation. Computer Methods in Applied Mechanics and Engineering, 300:748–769, March 2016. [3] B. Cockburn, D. A. Di Pietro, and A. Ern. Bridging the hybrid high-order and hybridizable discontinuous Galerkin methods. ESAIM: Mathematical Modelling and…

## 25 February – Buyang Li : A bounded numerical solution with a small mesh size implies existence of a smooth solution to the time-dependent Navier–Stokes equations

Buyang Li: Thursday 25 February at 14:00 We prove that for a given smooth initial value, if one finite element solution of the three-dimensional time-dependent Navier–Stokes equations is bounded by $M$ when some sufficiently small step size $\tau < \tau _M$ and mesh size $h < h_M$ are used, then the true solution of the Navier–Stokes equations with this given initial value must be smooth and unique, and is successfully approximated by the numerical solution.