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)



Registration is now closed.



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, 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
    • Alexandre Ern (Ecole des Ponts ParisTech), Finite element quasi-interpolation and best approximation, IHP, Amphi Darboux, TUE 13/9 15:00-16:00
    • 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
    • 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
  • 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 approximamtion 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
    • 24–28 Mini-course T2, Alfio Quarteroni (EPFL) with A. Manzoni and F. Negri, 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 and 14:00-17:15, WED 26/10 9:00-12:15 and 14:00-17:15
  • November and December
    • 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, MON 14/11 14:00-17:15, TUE 15/11 9:00-12:15 and 14:00-17:15, WED 16/11 9:00-12:15, THU 17/11 9:00-12:15 and 14:00-17:15
    • 21–25 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

Preliminary programme here


  • Lourenço Beirão da Veiga (Università Milano Bicocca), Virtual Element Methods
  • Bernardo Cockburn (University of Minnesota), An introduction to the HDG methods for PDEs
  • Robert Eymard (Université Paris-Est Marne la Vallée), Gradient schemes for linear and nonlinear elliptic and parabolic problems
  • Luca Formaggia (Politecnico di Milano), Interfacing models with different geometrical dimensions: the issue of defective interface conditions
  • Mark Gerritsma (TU Deflt), Mimetic spectral methods
  • Anthony Nouy (Ecole Centrale de Nantes), Low-rank and sparse tensor methods for stochastic and parametric PDEs
  • Gianluigi Rozza (SISSA), Reduced basis method and a posteriori error estimation for parametrized partial differential equations
  • 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


(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

Preliminary programme here 

Invited speakers:

  • Rémi Abgrall, Some recent developments on parameter free finite element like methods for unsteady hyperbolic problems
  • Susanne C. Brenner, Adaptive Methodes for Fourth Order Problems
  • Carsten Carstensen, Separate marking adaptive algorithms
  • Annalisa Buffa, to be announced
  • Clément Cancès, Entropy dissipative methods for parabolic problems
  • Bruno Desprès, Well-balanced schemes for Friedrichs systems and related problems
  • Thierry Gallouët, Discrete functional analysis
  • Jean-Luc Guermond, Invariant domains and continuous finite element approximation for hyperbolic systems
  • Alexander Linke, Towards pressure-robust mixed methods for the incompressible Navier-Stokes equations
  • Konstantin Lipnikov, Mimetic finite difference method for nonlinear parabolic equations: theory and applications
  • Jan Martin Nordbotten, Momentum-conserving discretizations for elasticity
  • Martin Vohralík, Guaranteed and robust a posteriori bounds for Laplace eigenvalues and eigenvectors
  • Thomas Wihler, Galerkin discretizations for finite time blow-up problems


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

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

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

Preliminary programme  here

Invited speakers:

  • Francisco Chinesta, Model order reduction in the factory of future: from data to knowledge
  • Albert Cohen, to be announced
  • Max Gunzburger, Reduced-order modeling for deterministic and stochastic anomalous diffusion problems
  • Jan S. Hesthaven, Reduced order models of Hamiltonian problems
  • Traian Iliescu, Large Eddy Simulation Reduced Order Models
  • Ioannis Kevrekidis, No equations, no variables: data, and the effective modeling of complex/multiscale systems
  • Bijan Mohammadi, Data Analytic Uncertaintly Quantification Cascade in Optimization
  • Mario Ohlberger, Localized model reduction beyond offline-online splitting
  • Anthony Patera, Model Order Reduction for Component-Based System Analysis
  • Clémentine Prieur, Goal-oriented error estimation, with application to sensitivity analysis
  • Serge Prudhomme, On  goal-oriented formulation for model reduction methods
  • Kristoffer Van Der Zee, Adaptive Modeling for Partitioned-Domain Concurrent Models
  • Alessandro Veneziani, Hierarchical Model Reduction techniques for hemodynamics: basics, isogeometric analysis, applications
  • Karen Willcox, Model reduction to support data-to-decision in engineering systems


(ME4) Workshop: Industry and mathematics

In collaboration with AMIES, SIMAI, SMAI

Dates: 21–24 November 2016, IHP (Paris)

Invited speakers:

  • Grégoire Allaire (Ecole Polytechnique), Rodin (robust optimal design in industry): an example of an industrial collaborative project on topology optimization of structure
  • Christophe Baehr (Météo France), to be announced
  • Ottavio Crivaro and Chiara Riccobene (MOXOFF), Where you don't expect numerical methods would help: Coffee, milk and  more !
  • Martin Ferrand (EDF R&D, MFEE), to be announced
  • 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
  • Franck Nicoud (University of Montpellier), Accounting for blood complexities in hemodynamics: issues and applications
  • Nicola Parolini (Politecnico di Milano), to be announced
  • Franck Pigeonneau (Surface du Verre et Interfaces, Saint-Gobain Recherche), Finite-element simulations of two-phase flows driven by the capillary forces
  • Christophe Prud'homme (Cemosis, le centre de modélisation et de simulation de Strasbourg, une agence math-entreprise en Alsace)
  • Paolo Ruffo (ENI), to be announced
  • Pierre Sochala (BRGM), Uncertaintly propagation using polynomial chaos for geoscience applications