Schools CEA - EDF - INRIA

Numerical analysis school 2022

Numerical analysis school 2022: contents, program, dates, practical information.

2022 summer school on numerical analysis

Certification of errors in numerical simulations

Preservation of invariants by post-processing and adaptivity (mesh, scheme, solvers, model) for industrial needs


Certification of errors in numerical simulations

Numerical simulation of partial differential equations has become an essential tool for finding approximate solutions to physical problems. It leads to several important questions:

  • What is the error in the numerical approximation?
  • Can we certify the result, give a safety margin?
  • Can we estimate the error in quantities of interest identified by the user (point value of the solution, flow through a part of the boundary)?
  • Can we have this information for an affordable cost, much smaller compared to the cost of the numerical simulation itself?

It is the theory of a posteriori error estimates which makes it possible to give affirmative answers to these questions. Exposing its latest advances, in detail for simple model problems, will be the central pillar of the proposed summer school.

Preservation of invariants by post-processing

The peculiarity of some a posteriori approaches is that they actually provide an improvement of the numerical approximation. These improvements make it possible to satisfy another highly desired property in numerical simulations: the preservation of invariants. For example, one can find a locally conservative field for a scheme non-conservative by construction via a local postprocessing which is already part of the a posteriori error evaluation. One day in the school will be devoted to this subject.

Adaptivity of mesh, scheme, solvers, and model

The theory of posteriori error estimates is also the basis of the concept of adaptivity of mesh, but also more broadly, including the scheme, the linear and nonlinear solvers, or the model. To give the participants an idea of the power of such an adaptivity, scientific seminars and industrial experiences will discuss these aspects.

Detailed descriptionPDF icon

Practical information


June 27 – July 1, 2022


Boulevard Gaspard Monge
91120 Palaiseau


If you wish to join, please fill the registration form Word icon and send it before June, 3, 2022 to Régis Vizet.


Summer schools secretary
Régis Vizet – CEA
tel: 01 69 26 47 45
Fax: 01 69 26 70 05

Coordinators of the numerical analysis 2022 school
Mickaël Abbas
Martin Vohralík

Registration fees (pre-tax price)

CEA, EDF, industry: 1200 euros
Academia / university & public research: 600 euros
Ph.D. students (a limited number): 300 euros


Monday, June 27 Tuesday, June 28 Wednesday, June 29 Thursday, June 30 Friday, July 1
Certification of errors Nonlinear and evolutive problems, identification of error components Errors in quantities of interest, model adaptivity, multiscale Convergence and optimality by mesh adaptivity Industrial employment
8h30-9h30 Breakfast coffee Breakfast coffee Breakfast coffee Breakfast coffee Breakfast coffee
9h30-12h Lectures
Alexandre Ern (Ecole des Ponts)
Alexandre Ern (Ecole des Ponts)
Ludovic Chamoin (ENS Paris Saclay)
Andreas Veeser (Università degli Studi di Milano)
9h30 François Madiot (CEA): A posteriori error estimates for mixed finite element discretizations of the neutron diffusion equations
11h Pascal Omnes (CEA): Adaptive simulations in incompressible fluid dynamics: issues and needs
12h-14h Lunch Lunch Lunch Lunch Lunch
14h-16h Computer tutorials Computer tutorials Computer tutorials Computer tutorials Examples
14h Romain Le Tellier (CEA): hp−AMR applied to the neutron transport equation discretized by a discontinuous Galerkin upwind scheme
15h Soleiman Yousef (IFPEN): Reservoir simulator runtime enhancement based on a posteriori error estimation techniques
16h-16h30 Coffee break Coffee break Coffee break Coffee break Coffee break
16h30-18h Scientific seminars Scientific seminars Scientific seminars Scientific seminars Discussion, conclusions, and perspectives
16h30 Théophile Chaumont-Frelet (Inria Sophia Antipolis): A posteriori error estimation via flux equilibration for magnetostatic problems Pierre Gosselet (Université de Lille): Parallel error estimation for primal and dual domain decomposition methods Valentine Rey (Université de Nantes): Error estimation in reliability analysis : multi-fidelity meta-models for the estimation of probability of failure Dirk Praetorius (Vienna University of Technology): On quasi-optimal computational costs of adaptive FEM
17h15 Sônia M. Gomes (Universidade Estadual de Campinas): A posteriori error estimator for a multiscale hybrid mixed method applied to Darcy’s flows Koondanibha Mitra (Hasselt University): Reliable, efficient, and robust a posteriori estimates for nonlinear elliptic problems Frédéric Legoll (École des Ponts ParisTech): Numerical simulations using the multiscale finite element method: a posteriori estimates and mesh adaptivity Roland Becker (Université de Pau et des Pays de l’Adour): Adaptive FEM for parameter identification problems