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Numerical Methods for Partial Differential Equations

Olivier Pironneau

• Contents
  • Forewords
  • Dates
  • Why go on the web?
  • Diploma
  • Who correct the exercises?
  • The content
  • What you need to do.
• LESSON: Introduction
  • Orientation
  • How to read a file
  • Gnuplot
  • batch file
• LESSON on freefem and gnuplot
  • Orientation
  • Problem statement
  • An example with freefem
  • Triangulation file
  • Read a Triangulation file
  • Display a Triangulation with gnuplot
  • Vizualisation of a function
  • Complement: the debugger gdb
    • The command where
    • Parameter passing in UNIX
  • Display of the level lines of a function
    • Principle: P1 interpolation
    • Error estimates
• Lesson: An explicit scheme for the wave eq.
  • The problem
  • The scheme
  • The program
  • Exercise
• Lesson: An implicit scheme
  • The Crank-Nicolson implicit scheme
  • Discretization in space
  • The conjugate gradient algorithm
    • Remark for non zero Dirichlet conditions
• Lesson: Automatic triangulation
  • Automatic triangulation of a square
    • The problem
    • Algorithm
    • The Delaunay criteria
  • Triangulation of a convex domain
    • Algorithm
  • Triangulation of a non convex domain
    • Algorithm
    • Generating interior points
  • Un premier module de triangulation automatique en C
  • Mesh Adaption
  • A Fast Finite Element Interpolator
• References
• About this document ...