Partial Differential Equations F3, 2002,
home, week 1,

Lectures and examination:
Claes Johnson
tel: 772 3518, 031-204327 (home)
Chalmers Finite Element Center Eklandagatan 80.
Lectures Monday and Thursday 10.00-11.45 in Kollektorn.

Richard Bergström
tel. 772 5314
Chalmers Finite Element Center Eklandagatan 80.
Exercise whole group: Wednesday 13-15 Kollektorn (except week 5: instead FL61, FL72)
Individual instruction: Wednesday 15-17 FL10.

Eriksson, Estep and Johnson: Computational Differential Equations (CDE), Studentlitteratur/Cambridge, 1996. CDE in brief

Optional complementing literature:
Eriksson, Estep and Johnson: Applied Mathematics: Body and Soul Springer 2003.
Selected chapters for download: What is Mathematics? Laplacian models, The Crash Model, The Solar System,
Lorenz and The Essence of Chaos, Navier-Stokes: quick and easy.


  1. Intro: Poisson, Conv-diffusion, Wave, Navier-Stokes
  2. Poisson's equation
  3. Heat equation
  4. Wave equation
  5. Convection-diffusion-reaction equation
  6. Maxwell's equations
  7. Schrödinger's equation
  8. Energy estimates
  9. Fundamental solutions
  10. Galerkin methods for discretization in time and space (finite element methods).
  11. Navier-Stokes with DOLFIN
Suggested CDE-reading:
Chapter 13 (Calculus review), 14-20 (Part. Diff. Eqns), 8-11 (Ordinary Diff. Eqns background).

Chalmers organization model: One Department-One Differential Equation.

Lecture notes from 2001:
Download lecture notes.

Exercise material:
Download exercises with hints and solutions.
Download problems with hints and solutions.

Project 1 Supporting code: MySvenssonSolver.m, MySvenssonSolver2.m, MySvenssonSolver3.m,
Project 2 Supporting code: MyPoissonSolver.m, MyHeatEqSolver.m, MyPLPoissonSolver.m, MyPLHeatEqSolver.m, MyPLWaveEqSolver.m,
Project 3 Navier-Stokes with DOLFIN (optional)

Written exam at the end of course, Friday Oct. 25 am (f"ormiddag) in V-building. The exam has 50 points. In addition you can get up to 5+5 points from two projects. Passing with grade 3 requires 25 points (adding points from exam and projects), passing with grade 4 requires 34, and grade 5 requires 43. If you reach the grade 4 this way you can also count points from a third project that you design yourself, and carry out after an ok from the examinator. This project, too, is worth up to 5 points. It is presented both in oral (Thursday Oct 18 in the lecture) and written (deliver with the exam) form. The point from the projects fade away after Oct 26 according to the formula bpoO26 x max(1-t^2,0) where bpoO26 means bonus points of October 26, and t is time in years. In particular, the points are gone after one year.
Written exam 011026 with solutions
Individual exam results.
Written exam 020115 with solutions
Individual 020115 exam results.


Last modified: Wed Aug 28 13:06:46 CEST 2002