IHP quarter on Numerical Methods for PDEs

September 5th - December 16th  2016



Numerical Analysis applied to the approximate solution of PDEs is a key discipline in Applied Mathematics.
Over the last few years, several new paradigms have appeared, leading to entire new families of discretization methods and solution algorithms. Simultaneously, the increased complexity of the underlying physical problems and the need to use simulators in many-query scenarios has prompted the study of model reduction techniques. Finally, a whole new approach to solution algorithms and adaptivity has been made possible by the recent advances in the context of a posteriori error analysis. The goal of this thematic quarter is to provide an opportunity to bring together leading scientists in the field of Numerical Analysis to discuss and disseminate the latest results and envisage new challenges in traditional and new application fields.
The project is structured around three main topics

  • Structure-preserving discretization methods (T1)
  • Model reduction (T2)
  • A posteriori error analysis (T3)



Applications for funding are now closed.

To participate in the activities that take place during thematic quarter, register here.



Steering committee D. A. Di Pietro (coordinator), A. Ern, L. Formaggia
Scientific committee R. Herbin, Y. Maday, D. Marini, R. Verfürth
Organizing committee P. F. Antonietti, S. Cordier, J. Droniou, R. Eymard, R. Fontanges, T. Lelièvre, B. Mohammadi, S. Perotto, G. Rozza



  • September
    • 05–09 Introductory school (ME1)
    • 12–16 Mini-course T1, Daniele Di Pietro (University of Montpellier),  Hybrid High-Order methods, IHP, Amphi Darboux, TUE 13/9 9:00-12:15, WED 14/9 9:00-12:15. Slides can be downloaded here
    • Alexandre Ern (Ecole des Ponts ParisTech), Finite element quasi-interpolation and best approximation, IHP, Amphi Darboux, TUE 13/9 15:00-16:00. Slides can be downloaded here. Se also here for a bibliographic reference
    • 19–23 Mini-course T1-T2, Daniele Boffi (Università di Pavia), Finite element approximation of eigenvalue problems, IHP, Amphi Darboux, TUE 20/09 9:00-12:15, WED 21/09 9:00-12:15, THU 22/09 9:00-12:15. Slides and other supports can be downloaded here.
    • 26–30 Mini-course T1-T3, Erik Burman (University College London), Stabilized finite element methods for ill-posed problems, IHP, Amphi Darboux, TUE 27/09 9:00-12:15, WED 28/09 9:00-12:15, THU 29/09 9:00-12:15. Slides can be downloaded here.
  • October
    • 03–07 Conference T1 (ME2)
    • 10–14 Mini-course T2, Jean-Frédéric Gerbeau (INRIA), Direct, inverse and reduced-order modeling for the cardiovascular system, IHP, Amphi Darboux, MON 10/10 14:00-17:15, TUE 11/10 14:00-17:15, WED 12/10 14:00-17:15
    • 17–21 Mini-course T2, Albert Cohen (UPMC), High dimensional approximation of parametric PDE's - theory and algorithms, IHP, Amphi Darboux, TUE 18/10 9:00-12:15, WED 19/10 9:00-12:15, THU 20/10 9:00-12:15. Slides can be downloaded here.
    • 24–28 Mini-course T2, Alfio Quarteroni (EPFL) with Andrea Manzoni, Functional, geometric, and  algebraic reduction strategies for large-scale computing, IHP, Amphi Darboux, MON 24/10 14:00-17:15, TUE 25/10 9:00-12:15, WED 26/10 9:00-12:15
  • November and December
    • 02-04 Junior colloquium on H(div) and H(curl) elements, IHP, Amphi Darboux, WED 02/11 14:00-17:30, THU 03/11 14:00-17:30,FRI 04/11 10:00-12:00
    • 4 Histoire des équations différentielles aux dérivées partielles : méthodes numériques et analytiques, IHP Amphi Darboux, organized by F. Brechenmacher. Programme available here. FRI 04/11 14:00-18:30.
    • 7–10 Conference T2 (ME3)
    • 14–18 Mini-course T3, Martin Vohralík (INRIA), A posteriori error estimates for efficiency and error control in numerical simulations, IHP, Amphi Darboux, TUE 15/11 9:00-12:15, WED 16/11 9:00-12:15, THU 17/11 9:00-12:15
    • 21–23 Workshop Industry and mathematics (ME4)
    • 28/11–2 Mini-course T1-T3, Roland Becker (UPPA), Adaptive finite element methods for boundary and interface conditions, IHP, Amphi Darboux, MON 28/11 14:00-17:15, TUE 29/11 9:00-12:15, WED 30/11 9:00-12:15


Long-term invitations

  • Paola Antonietti (Politecnico di Milano)
  • Daniele Boffi (Università di Pavia)
  • Carsten Carstensen (Humboldt-Universität zu Berlin)
  • Victor Calo (King Abdullah University of Science and Technology)
  • Jérôme Droniou (Monash University)
  • Luca Formaggia (Politecnico di Milano)
  • Jean-Luc Guermond (Texas A&M University)
  • Ricardo Nochetto (University of Maryland)
  • Martin Nordbotten (University of Bergen)
  • Mario Ohlberger (Westfälische Wilhelms-Universität Münster)
  • Gianluigi Rozza (SISSA, Trieste)
  • Andreas Veeser (Università degli Studi di Milano)
  • Christian Vergara (Politecnico di Milano)


Main events

(ME1) Introductory school

Dates: September 5–9, 2016, Institut d'Études Scientifiques de Cargese (Corse)

Chair: D. Marini

Organizers: D. A. Di Pietro, L. Formaggia, A. Ern

Programme here


  • Lourenço Beirão da Veiga (Università Milano Bicocca), Virtual Element Methods. Slides can be downloaded here
  • Bernardo Cockburn (University of Minnesota), An introduction to the HDG methods for PDEs. Lecture notes can be downloaded here (the password will be communicated at the beginning of the lecture)
  • Robert Eymard (Université Paris-Est Marne la Vallée), Gradient schemes for linear and nonlinear elliptic and parabolic problems. Slides can be downloaded here
  • Luca Formaggia (Politecnico di Milano), Interfacing models with different geometrical dimensions: the issue of defective interface conditions
  • Mark Gerritsma (TU Deflt), Mimetic spectral methods. Slides can be downloaded here
  • Anthony Nouy (Ecole Centrale de Nantes), Low-rank and sparse tensor methods for stochastic and parametric PDEs. Slides can be downloaded here
  • Gianluigi Rozza (SISSA), Reduced basis method and a posteriori error estimation for parametrized partial differential equations. Slides can be downloaded here
  • Andreas Veeser (Università degli Studi di Milano), Basic of adaptive finite element methods
  • Martin Vohralík (INRIA), A posteriori error estimates and adaptive error components balancing in numerical simulations. Slides can be downloaded here


(ME2) Conference: Advanced numerical methods: recent developments, analysis, and applications

Dates: 3–7 October 2016, IHP (Paris)

Organizers: P. F. Antonietti, J. Droniou, R. Eymard

Programme here 

Invited speakers:

  • Rémi Abgrall (Universität Zürich), Some recent developments on parameter free finite element like methods for unsteady hyperbolic problems. Slides can be downloaded here
  • Susanne C. Brenner (Louisiana State University), Adaptive Methodes for Fourth Order Problems
  • Carsten Carstensen (Humboldt Universität zu Berlin), Separate marking adaptive algorithms
  • Clément Cancès (INRIA Lille), Entropy dissipative methods for parabolic problems. Slides can be downloaded here
  • Bruno Desprès (Université Pierre et Marie Curie), Well-balanced schemes for Friedrichs systems and related problems. Slides can be downloaded here
  • Thierry Gallouët (Aix-Marseille Université), Discrete functional analysis
  • Jean-Luc Guermond (Texas A&M), Invariant domains and continuous finite element approximation for hyperbolic systems. Slides can be downloaded here
  • Alexander Linke (WIAS Berlin), Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations. Slides can be downloaded here
  • Konstantin Lipnikov (Los Alamos National Laboratory), Mimetic finite difference method for nonlinear parabolic equations: theory and applications
  • Jan Martin Nordbotten (University of Bergen), Momentum-conserving discretizations for elasticity
  • Martin Vohralík (INRIA), Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors. Slides can be downloaded here
  • Thomas Wihler (Universität Bern), Galerkin discretizations for finite time blow-up problems

Slides from contributed talks: G. Barrenechea, C. Chainais-Hillairet, F. Chave, D. A. Di Pietro, S. Gomes, J. Hennicker, B. Jin, I. Mazzieri


(ME3) Conference: Recent developments in numerical methods for model reduction

Dates: 7–10 November 2016, IHP (Paris)

Organizers: T. Lelièvre, S. Perotto, G. Rozza

Programme here

Book of abstracts here

Invited speakers:

  • Francisco Chinesta (Ecole Centrale Nantes), Model order reduction in the factory of future: from data to knowledge
  • Albert Cohen (Université Pierre et Marie Curie), Data assimilation, parameter estimation and reduced modeling
  • Max Gunzburger (Florida State University), Reduced-order modeling for deterministic and stochastic anomalous diffusion problems
  • Jan S. Hesthaven (Ecole Polytechnique Fédérale Lausanne), Reduced order models of Hamiltonian problems
  • Traian Iliescu (Virginia Tech), Large Eddy Simulation Reduced Order Models
  • Ioannis Kevrekidis (Princeton University), No equations, no variables: data, and the effective modeling of complex/multiscale systems
  • Bijan Mohammadi (Université de Montpellier), Data Analytic Uncertaintly Quantification Cascade in Optimization
  • Mario Ohlberger (WWU Münster), Localized model reduction beyond offline-online splitting
  • Anthony Patera (MIT), Model Order Reduction for Component-Based System Analysis
  • Antonio Huerta (Universitat Politècnica de Catalunya), Generalized parametric solutions in Soktes flow and complex domains
  • Serge Prudhomme (Polytechnique Montréal), On  goal-oriented formulation for model reduction methods
  • Kristoffer Van Der Zee (The University of Nottingham), Adaptive Modeling for Partitioned-Domain Concurrent Models
  • Alessandro Veneziani (Emory University), Hierarchical Model Reduction techniques for hemodynamics: basics, isogeometric analysis, applications


(ME4) Workshop: Industry and mathematics

In collaboration with AMIES, SIMAI, SMAI

Dates: 21–23 November 2016, IHP (Paris)

Preliminary programme here

Invited speakers:

  • Grégoire Allaire (Ecole Polytechnique), The RODIN project: an example of research collaboration with industry in the context of shape and topology optimization of structures
  • Christophe Baehr (Météo France), Stochastic engineering for the atmospheric sciences
  • Chiara Riccobene (MOXOFF), Where you don't expect numerical methods would help: Coffee, milk and  more!
  • Martin Ferrand (EDF R&D, MFEE), Development of an integral formulation for flows in media cluttered with obstacles in an open-source CFD code
  • Sylvie Granet (EDF, LAMSID), Modelling of Geological Nuclear Waste Disposal : Some Thermo-Hydro-Méchanical problems in porous media
  • Christian Mariotti (CEA), A formulation of the discrete element method
  • Roland Masson (Université de Nice), Modelization and discretization of multiphase flows in fractured porous media
  • Edie Miglio (MOX) and Paolo Ruffo (ENI), Some issues in Geophysical and Geological Modeling
  • Franck Nicoud (University of Montpellier), Accounting for blood complexities in hemodynamics: issues and applications
  • Nicola Parolini (Politecnico di Milano), Fluid-structure interaction and geometrical multi-scale models for packaging systems
  • Pierre Saramito (CNRS, LJK Grenoble), On a collaboration with Saint-Gobain Recherche for surface tension modeling by phase field or level-set, and a discontinuous Galerkin approximation
  • Christophe Prud'homme (Cemosis, le centre de modélisation et de simulation de Strasbourg, une agence math-entreprise en Alsace), A zoom on some Math-Entreprise collaborations at the Center of Modeling and Simulation of Strasbourg (Cemosis)
  • Pierre Sochala (BRGM), Uncertaintly propagation using polynomial chaos for geoscience applications

    Funded by ANR