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Internal Seminar

Internal Seminar Calendar

2024 – 2025

  • 6th May 2025 – 10h00 to 12h00 Daniel Zegarra Vasquez: Efficient numerical simulation of single-phase flow in three-dimensional fractured porous media
  • 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: equations: how to turn a numerical simulation into a theorem. (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

February 20 – Thirupathi Gudi: An energy space based approach for the finite element approximation of the Dirichlet boundary control problem.

Thirupathi Gudi: Tuesday 20 February at 3 pm, A415 Inria Paris. In this talk, we review some approaches for formulating the Dirichlet boundary control problem and then we present a new energy space based approach. We show that this new approach allows high regularity for both optimal control and the optimal state. Using, the optimality conditions at continuous level, we propose a finite element method for numerical solution and derive subsequent error estimates. We show some numerical experiments to illustrate the method.

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February 15 – Franz Chouly: About some a posteriori error estimates for small strain elasticity

Franz Chouly: Thursday 15 February at 2 pm, A415 Inria Paris. In the first part of this talk, we will present a residual based a posteriori error estimate for contact problems in small strain elasticity, discretized with finite elements and Nitsche’s method. Upper and lower bounds are established under a saturation assumption. This theoretical results will be illustrated by some numerical experiments (joint work with Mathieu Fabre, Patrick Hild, Jérôme Pousin and Yves Renard). In the second part of this talk, we will present preliminary results on goal oriented error estimates for soft-tissue biomechanics, still under small strain assumptions. The performance of the Dual Weighted Residual method will be assessed for two simplified scenarios involving tongue muscular activation, and contraction of the arterial wall. Open mathematical questions and the potential interest of such a methodology for computational biomechanics will be discussed (joint work with Stéphane Bordas, Marek Bucki, Michel Duprez, Vanessa Lleras, Claudio Lobos, Alexei Lozinski, Pierre-Yves Rohan and Satyendra Tomar).

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November 2 – Hend Benameur: Identification of parameters, fractures ans wells in porous media

Hend Benameur: Thursday 2 November at 11 am, A415 Inria Paris. We are interested in some inverse problems in porous media: parameter estimation, fracture identification and wells location. All these problems are formulated as optimization problems. The main and common tool in the developed techniques is “ the gradient” of a convenient function. An adaptive parameterization algorithm is developed, implemented and applied for the estimation of scalar and vector parameters in porous media. Values of parameters and shapes of hydrogeological zones are unknown. The main tool in the adaptive parameterization approach is a refinement indicator: Once the identification problem is set as a minimization of an objective function, the question is what is the effect on this function of allowing discontinuity of the parameter in some candidate location? Refinement indicators give the answer to this question . Since fractures are characterized by discontinuities, the idea is to extend previous indicators to locate fractures. We define fracture indicators and we proceed in an iterative way in order to identify fractures in porous media. The topological sensitivity analysis method has been recognized as a promising tool to solve topology optimization problems. It consists to provide an asymptotic expansion of a shape functional with respect to the size of a small hole created inside the domain. To solve the inverse problem where both parametrization and well’s location are unknown, we incorporate the topological gradient approach in the adaptive parametrization algorithm; results are promising.

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October 10 – Peter Minev: Recent splitting schemes for the incompressible Navier-Stokes equations

Peter Minev: Tuesday 10 October at 11 am, A415 Inria Paris. The presentation will be focussed on two classes of recently developed splitting schemes for the Navier-Stokes equations. The first class is based on the classical artificial compressibility (AC) method. The original method proposed by J. Shen in 1995 reduces the solution of the incompressible Navier-Stokes equations to a set of two or three parabolic problems in 2D and 3D correspondingly. Unfortunately, its accuracy is limited to first order in time and can be extended further only if the resulting scheme involves an elliptic problem for the velocity vector. Recently, together with J.L. Guermond (Texas A&M University) we proposed a scheme that extends the AC method to any order in time using a bootstrapping approach to the incompressibility constraint that essentially requires to solve only a set of parabolic equations for the velocity. The conditioning of the corresponding linear systems is therefore O(Δth^-2). This is generally better than solving a parabolic equation for the velocity and an elliptic equation for the pressure required by the various projection schemes that are perhaps the most popular approach at present. Besides, the bootstrapping algorithm allows to achieve any order in time, subject to some initialization conditions, in contrast to the projection methods whose accuracy seems to be essentially limited to second order on the velocity in the L2 norm. The second class of methods is based on a novel approach to the Navier-Stokes equations that reformulates them in terms of stress variables. It was developed in a recent paper together with P. Vabishchevich (Russian Academy of Sciences). The main advantage of such an approach becomes clear when it is applied to fluid-structure interaction problems since in such case the problems for the fluid and the structure, both written in terms of stress variables,…

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September 18 – Théophile Chaumont: High order finite element methods for the Helmholtz equation in highly heterogeneous media

Théophile Chaumont: Monday 18 September at 1 pm, A415 Inria Paris. Time-harmonic wave propagation problems are costly to solve numerically since the corresponding PDE operators are not strongly elliptic, and as a result, discretization methods might become unstable. Specifically, the finite element solution is quasi-optimal (almost as good as the best approximation the finite element space can provide) only under restrictive assumptions on the mesh size. If the mesh size is too large, stability is lost, and the finite element solution can become completely inaccurate, even when the best approximation is. This phenomenon is called the « pollution effect » and becomes more important for larger frequencies. For the case of wave propagation problems in homogeneous media, it is known that high order finite element methods are less sensitive to the pollution effect. For this reason, they are employed in a wide range of applications, as the corresponding linear systems are smaller and easier to solve. In this talk, we investigate the use of high order finite element methods to solve wave propagation problems in highly heterogeneous media. Since the heterogeneities of the medium can exhibit small scale features, we consider « non-fitting » meshes, that are not aligned with the physical interfaces of the medium. Instead, the parameters defining the medium of propagation can be discontinuous inside each element. We propose a convergence analysis and draw two main conclusions: – the asymptotic convergence rate of the proposed finite element method is suboptimal due to the lack of regularity of the solution inside each cell – the pollution effect is greatly reduced by increasing the order of discretization. We illustrate our main conclusions with geophysical application benchmarks. These examples confirm that higher order methods are more efficient than linear finite elements.

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June 22 – Valentine Rey: Goal-oriented error control within non-overlapping domain decomposition methods to solve elliptic problems

Valentine Rey: Thursday 22 June at 3 pm, A415 Inria Paris. Domain decomposition methods are robust and efficient methods to solve mechanical problems with several million degrees of freedom. Taking advantage of increasing performances of computers, they exploit the clusters-parallel architecture and are numerically scalable. Verification has been widely developed since 1980’s and proposes tools to estimate the distance between the unknown exact solution of continuous problem and the computed solution. Among those techniques, estimators based on error in constitutive relation provide constant-free upper bounds and are available for varied range of problems. In this talk, we present techniques for steering parallel computation by objective of accuracy on quantities of interest. It relies on a parallel error estimator that provides strict guaranteed upper bound and separates the algebraic error (due to the use of iterative solver) from the discretization error (due to the finite element method). This estimator enables to adapt the solver’s stopping criterion to the discretization, which avoids over resolution and useless iterations. In [*], the estimator is used for goal-oriented error estimation and classical bounds for quantities of interest are rewritten in order to separate sources of error. Finally, we benefit the information provided by the error estimator and the Krylov subspaces built during the resolution to set an auto-adaptive strategy (adaptive remeshing and recycling search directions). *V. Rey, P. Gosselet, C. Rey, Strict bounding of quantities of interest in computations based on domain decomposition, Computer Methods in Applied Mechanics and Engineering. 2015 Apr 15;287:212-28

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29 June – Gouranga Mallik: A priori and a posteriori error control for the von Karman equations

Gouranga Mallik: Thursday 29 June at 3pm, A415 Inria Paris. In this work we consider a priori and a posteriori error control for the nonsingular solution of von Karman plate bending problem. Conforming and nonconforming finite element methods are employed. Existence, uniqueness and error estimates for the discrete solution are presented. We discuss an abstract framework for a posteriori error control which includes conforming and nonconforming finite element methods. This allows us to compute reliable and efficient local estimators. The key ingredients in establishing well-posedness of the discrete problem rely on the linearization of the continuous problem and suitable enrichment operator. Numerical experiments are performed to justify the theoretical results.

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June 15 – Patrik Daniel: An adaptive hp-refinement strategy with computable guaranteed error reduction factors

Patrik Daniel: Thursday 15 June at 3:30pm, A415 Inria Paris. We propose a new practical adaptive refinement strategy for hp-finite element approximations of elliptic problems. Following some recent theoretical developments in polynomial-degree-robust a posteriori error analysis, we solve two complementary classes of discrete local problems on the vertex-based patches. The first class involves the solution on each patch of a mixed finite element problem with homogeneous Neumann boundary conditions, which leads to an H(div,Ω)-conforming equilibrated flux. This in turns yields a guaranteed upper bound on the error and serves to mark elements for refinement via a Dörfler bulk criterion. The second class of local problems involves the solution, on each marked patch only, of two separate primal finite element problems with homogeneous Dirichlet boundary conditions, which serve to decide between h-, p-, or hp-refinement. Altogether, we show that these ingredients lead to a computable error reduction factor; we guarantee that while performing the hp-adaptive refinement as suggested, the error will be reduced at least by this factor on the next hp-mesh. In a series of numerical experiments in two space dimensions, we first study the accuracy of our predicted reduction factor: in particular, we measure the ratio of the predicted reduction factor relative to the true error reduction, and we find that it is very close to the optimal value of one for both smooth and singular exact solutions. Finally, we study the overall performance of the proposed hp-refinement strategy on some test cases, for which we observe effectivity indices very close to one and exponential convergence rates.

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June 15 – Jad Dabaghi: Adaptive inexact semi-smooth Newton methods for a contact between two membranes

Jad Dabaghi: Thursday 15 June at 3pm, A415 Inria Paris. We propose an adaptive inexact version of a class of semi-smooth Newton methods. As a model problem, we consider the system of variational inequalities describing the contact between two membranes and its finite element discretization. Any iterative linearization algorithm like the Newton-min, Newton-Fisher Burmeister is taken into account, as well as any iterative linear algebraic solver. We prove an a posteriori error estimate between the exact solution and the approximate solution which is valid on any step of the linearization and algebraic resolution. This estimate is based on discretization and algebraic flux reconstructions, where the latter one is obtained on a hierarchy of nested meshes. The estimate distinguishes the discretization, linearization, and algebraic components of the error and allows us to formulate adaptive stopping criteria for both solvers. Numerical experiments for the semi-smooth Newton-min algorithm in combination with the GMRES solver confirm the efficiency of the method.

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