Advanced Methods for the Diffusion Equation on General Meshes

Workshop on
Advanced methods for the diffusion equation on general meshes

Workshop date and place

Monday July 5 th and Tuesday July 6th, 2010, 9:00 - 18:00
Seminar room towers 15-16, 3rd floor, room 309
Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie (Paris 6)
4 place Jussieu, 75252 Paris, FRANCE
access details
Access at the entrance of the campus on the left by the lift tower 26 is easy

Motivations

Numerical methods on general meshes are the subject of on-going research in academic and industrial laboratories. This is motivated by the need of improved methods and algorithms for practical computations. During this workshop, experts will meet to discuss state of the art and new trends.

Theoretical derivation

Practical implementation issues

Results and open question

A special session will be dedicated to the presentation of the benchmark problem addressed at the FVCA6 conference.

Notice that another Workshop will be organised in September 2010, the 9th and 10th, on similar subjects.

Main speakers

Konstantin Lipnikov, T5, LANL, USA
Robert Eymard , Université Paris-Est Marne la Vallée
Franco Brezzi , Insituto Universitario di Studi Superiori, Pavia, Italy
Florence Hubert , Laboratoire d'analyse, probabilités et topologie, CMI, Marseille

Full list of speakers

Christophe Fochesato (CEA)
Gerald Samba (CEA)
Vincent Siess (CEA)
Bernard Rebourcet (CEA)
Pierre Henri Maire (CEA-CESTA, Bordeaux)
Emmanuel Franck (thésard, CEA-P6)
Francois Hermeline (CEA)
Pascal Omnes (CEA)
Christophe Le Potier (CEA)
Daniele Di Pietro (IFP)
Léo Agélas (IFP)
Martin Vohralik (P6)
Jérôme Jaffré (Inria)
Claire Chainais-Hillairet (Univ. Clermont-Ferrand)
Raphaele Herbin (Univ. Marseille)

Titres et résumés

List of participants

Program Monday

10:00-10:45	Konstantin Lipnikov	Mimetic finite difference method for diffusion problems
10:45-11:15	Daniele Di Pietro	Cell centered Galerkin methods
11:15-11:45	Coffee break
11:45-12:15	Pascal Omnes	Numerical solution of elliptic equations by a hybrid diamond / discrete duality finite volume scheme
12:15-12:45	Claire Chainais-Hillairet	Finite volume schemes for an elliptic-parabolic model describing miscible displacement in a porous medium
12:45-13:15	Pierre-Henri Maire	A cell-centered anisotropic diffusion scheme on two-dimensional unstructured meshes
13:15-14:45	Lunch break
14:45-15:30	Florence Hubert	Un schéma DDFV pour des équations elliptiques linéaires et non linéaires en 3D
15:30-16:00	Vincent Siess	Un schéma de volumes finis linéaire respectant le principe du maximum sur des maillages déformés
16:00-16:30	Coffee break
16:30-17:00	Jérôme Jaffré	Mixed finite elements on hexahedral meshes
17:00-17:30	Bernard Rebourcet	An old scheme adapted to new problems
17:30-18:00	Martin Vohralik	Lowest-order mixed finite element methods: implementation with one unknown per element, local flux expressions, positivity, polygonal meshes, and relations to other methods

Program Tuesday

10:00-10:45	Franco Brezzi	Mimetic Finite Differences and Nonconforming Finite Elements
10:45-11:15	François Hermeline	Un point sur les methodes de type volumes finis en dualite discrete (DDFV) en dimension trois
11:15-11:45	Coffee break
11:45-12:15	Emmanuel Franck	Schémas asymptotic preserving pour les modèles aux moments sur maillages non structurés
12:15-12:45	Christophe Le Potier	Correction non linéaire et principe du maximum pour la discrétisation d'opérateurs de diffusion avec des schémas volumes finis centrés sur les mailles
12:45-13:15	Christophe Fochesato	Résolution d'une équation de diffusion magnétique par la méthode des éléments finis mixtes hybrides
13:15-14:45	Lunch break
14:45-15:30	Robert Eymard	A symmetric and convergent finite volume scheme with 27-point stencil for 3D distorted hexahedral meshes
15:30-16:00	Gérald Samba	A fix to avoid violation of the maximum principle
16:00-17:00	Coffee break and lab presentation
17:00-17:30	Raphaèle Herbin	Finite volume schemes for the biharmonic problem on general polygonal meshes
17:30-18:00	Léo Agélas	The G method for diffusion problem on general meshes

Registration

There is no workshop fee. Registration by sending an e-mail to colloque_diffusion@ann.jussieu.fr is however compulsory. It gives access to the talks, coffee breaks and lunches.

Organizers

Bruno Després, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris 6), Paris, France
Martin Vohralík, Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie (Paris 6), Paris, France

Scientific committee
Robert Eymard, Bernard Rebourcet, Jacques Segré, Roland Masson, Raphaèle Herbin, Florence Hubert, Bruno Després, Martin Vohralik

Concurrent Workshop
A posteriori error estimates and mesh adaptivity for evolutionary and nonlinear problems

The support of

Université Pierre et Marie Curie,

Commissariat à l'Energie Atomique, et aux Energies Alternatives,

Institut Français du Pétrole,

Gamni/Smai and

Laboratoire Jacques-Louis Lions is gratefully acknowledged.

For all questions, send an e-mail to colloque_diffusion@ann.jussieu.fr.

First update on July 2, 2010.