The aim of the CIMPA Summer School in IIT Bombay is to provide the participants with an overview of the modern techniques that allow one to address the computational challenges that are encountered in different applications.

The topics in the school are aimed to cover the latest in the state of the art numerical schemes in real life applications and will be taught in English language.

Courses

The courses will be taught in English language.

Main School Topics

1. FEM : conforming and non standard including non-conforming, mixed, DG, etc with applications.
Speakers
o Susanne Brenner & Li-Yeng Sung (Louisiana University)
o Jean-Claude Nedelec (Rennes and Ecole Polytechnique)


2. Adaptive FEM, Problem reductions with FEM, Multi scale FEM.
Speakers
o Cartsen Carstensen (Humboldt University - Berlin)
o Andreas Veeser (Milano)
o Martin Vohralik (INRIA)


3. Introduction to FEM for Finance, Parallel Computing & Applications.
Speakers
o Olivier Pironneau (U-Paris VI)
o Frederic Hecht (LJLL-UPMC)


4. Optimal control & Optimal shape design.
Speakers
o Gregoire Allaire (Ecole Polytechnique)
o Jean-Pierre Raymond (Toulouse)


5. Fluid structure interaction, complex fluid, multi-scale simulations and applications of FEM.
Speakers
o Roland Becker (U Adour (Pau))
o Alexei Lozinski (U Besancon)
o Bertrand Maury (U Paris-Sud)

Pre-School Topics
A quick introduction to Sobolev spaces, Review of Elliptic PDE: existence of unique weak solution, regularity. Quick review of FEM: Cea's Lemma, Aubin-Nitsche duality technique, convergence rates. A posteriori error analysis, reliability, efficiency, Adaptive finite element methods for elliptic PDEs: basics, Medius Analysis, Discontinuous Galerkin FEM for elliptic PDE and FEM for Navier Stokes Equations and Introduction to Optimal Control Problems governed by PDE . Introduction to Freefem++.

Speakers
• Prof. T. Gudi (IISc, Bangalore)
• Prof. S. Kesavan (CMI, Chennai)
• Prof. Amiya K. Pani (IIT Bombay)
• Prof. Mythily Ramaswamy (TIFR CAM, Bangalore)
• Prof. M. Vanninathan (TIFR CAM, Bangalore)
• Prof. A. VasudevaMurthy (TIFR CAM, Bangalore)
• Prof. Raju K. George (IIST, Trivandrum)
• Prof. Rajen Sinha (IIT Guwahati)


Lab Sessions
• Prof. Sai Jagan Mohan (BITS, Pilani)
• Prof. D. Palla (BITS, Goa)

Committees

Co-ordinators
o Dr. Neela Nataraj, Professor, Department of Mathematics, Indian Institute of Technology Bombay, Powai, Mumbai 400076. E-mail: neela@math.iitb.ac.in

o Prof. O. Pironneau, Professeur, Emérite de l'Universit Pierre et Marie Curie au Laboratoire Jacques-Louis Lions, LJLL-UPMC, Boite 187, Jussieu, F-75252 Paris Cedex 5. E-mail: Olivier.Pironneau@upmc.fr


Scientific Committee
o Prof. Susanne C. Brenner, Michael F. and Roberta Nesbit McDonald Professor, Louisiana State University, Baton Rouge, USA
o Dr. Neela Nataraj, Professor, Indian Institute of Technology Bombay, India
o Prof. O. Pironneau, Professeur, Emérite de l'Universite Pierre et Marie Curie au Laboratoire Jacques-Louis Lions


Local Organizing Committee
o Dr. Thirupathi Gudi, Assisant Professor, Department of Mathematics, Indian Institute of Science Bangalore
o Dr. Neela Nataraj, Professor, Department of Mathematics, Indian Institute of Technology Bombay, Mumbai
o Prof. Amiya K. Pani, Institute Chair Professor, Department of Mathematics, Indian Institute of Technology Bombay, Mumbai
o Prof. O. Pironneau, Professeur, Emérite de l'Universite Pierre et Marie Curie au Laboratoire Jacques-Louis Lions
o Prof. Mythily Ramaswamy, TIFR CAM, Bangalore