### Partial Differential Equations - Project Course ENM, TMA632, Quarter II Fall 2009.

**Lectures and examination:**

Nils Svanstedt

tel: 772 5346

nilss@chalmers.se

**Lectures:**

Wednesdays 10-11.45 in in MVF 21 and Fridays 10-11.45 in MVF 33 .

(Note Friday the first week the lecture is in Pascal 10-11.45.)
**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

**An article on:**

Adaptive methods for Computational Fluid Dynamics (CFD)

**A small note on:**

adaptive algorithms

**Some m-files for adaptive meshrefinement: (Test by running the script file run.m) **

run.m

Assembler_1.m

MyFirst2DPoissonAssembler.m

S_shapeuniform.m

S_shapeadaptiv.m

L_shapeuniform.m

L_shapeadaptiv.m

f.m

**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, biharmonic equation.

**Examination:**

1. Completed ODE project (see below).

2. Completed PDE project (see below).

**Projects:**

ODE-Project Adaptive ode-solver

PDE project See list of PDE projects

Last modified: Fri 10 October 2008