Introduction to finite
General information: See the syllabus
The course will follow the book by
S.C. Brenner and L.R. Scott : The Mathematical theory of
finite element methods, springer-verlag 1994.
The scilab software can be
Classes start Feb. 9, 2009
Course : Friday 8-10, Lab. Dieudonné; P-E Jabin
Exercises : Monday 15:15-17:15, EPU; A. Sangam
Friday 10:15-12:15, Lab. Dieudonné; V. Dolean
Office hours : P-E Jabin : Thursday 15:15-17:15
Homework : 4 pages max. on chapt. 1 and chapt. 2 (up to 2.4 included). Due friday 13th march.
Exercises : 1st class and correction, 2nd class and correction, 3rd class and correction
Introduction to scilab and computer implementation : Introduction 1st class
Short Program : it may be slighty modified/updated along the course. The section and chapter numbers are always given
with respect to Brenner-Scott.
1st class :
0. Quick presentation of the course.
1. Derivation of diffusion or heat equation from discrete jump processes
: first the simple brownian case and then non homogeneous diffusion with
2. Elliptic problems introduced as stationary solutions or asymptotic in
time of diffusion problems. Formal proof based on the energy dissipation for the asymptotic
3. Other examples without full derivation : Black and Scholes for
finance, fluid mechanics (Navier-Stokes only).
2nd Class : Chapter 0 of Brenner-Scott, Introduction to finite elements
1. section 0.1 : Weak formulation
2. section 0.2 : Ritz-Galerkin approximation
3. section 0.4 : The finite element method
4. section 0.6 : Computer implementation
3rd class : End of chapter 0, Error Estimates
1. section 0.6 : the sequel of the 2nd class
1. section 0.5 : Comparison with other methods
2. section 0.3 and 0.7 : Error estimates
4th class : Chapter 3, Construction of a finite element space
1. section 0.8 : Weighted norm estimates
2. section 3.1 : definition of a finite element
3. section 3.2 : triangular
5th class : End of chapter 3
1. section 3.3 : the interpolant
2. section 3.5 : rectangular elements and some
words of 3.6.
3. Crash course on numerical analysis for matrices : 1st part.
1. Crash course on numerical analysis for matrices : 2nd part.
2. Summary of chapt. 1
7th class :
1. Summary of standard Hilbert theory 2.1 to 2.4.
2. Chapter 2, from 2.5.
8th class :
1. End of chapter 2.
2. Summary of 4.1, 4.2
3. Section 4.3
1. End of section 4.3
2. Part of 4.4
3. Section 5.1
Chapter 5 at least
the end of 5.1, and then 5.3, 5.4 solving Poisson equation and if there is more time : 5.2
Neumann problem, 5.5 regularity estimates for Poisson.