### Partial Differential Equations- Scientific Computing TM/ENM, TMA482, Winter quarter 2007.

**Lectures and examination:**

Nils Svanstedt

tel: 772 5346

nilss@math.chalmers.se

Lectures: Monday 10-12 in MV-F32 and Thursday 10-12 in in MV-F32.

**Computer Sessions (jointly with TMA632 Project Course PDE):**

Karin Kraft

tel. 772 5328

kakr@math.chalmers.se

Sessions/Lectures: Monday 13-15 in MV-F24 and Friday 10-12 in in MV-F24.

**Literature:**

Computational
Differential Equations (CDE), Studentlitteratur/Cambridge, 1996.

** Software (for ODE project):**

Computer Sessions (session E8)

Start doing this session as a preparation for your ODE project.

**Software (for PDE project):**

Puffin

**An article on:**

Adaptive methods for parabolic problems

**A small note on:**

adaptive algorithms

**A small note on:**

adaptivity for ode's

**A small note on:**

piecewise linear approximation in 1d,

**Content:**

- A posteriori error analysis for ordinary differential equations.
- Stability estimates
- Duality and adjoint operators.
- A priori error analysis for partial differential equations
- A posteriori error analysis for partial differential equations
- Adaptive finite element methods
- Stabilization methods like streamline-diffusion.
- FEM for various types of problems like wave propagation, incompressible Navier-Stoke equations,

elliptic eigenvalue problems, convection-diffusion-reaction problems, Schrödinger equations.

**Examination:**

Written examination on theory and completed ODE project (see below).

**Projects:**

ODE-Project Adaptive ode-solver

Last modified: Wed 11 15:07:26 MET DST 2006