===== Literature =====

**SM** [[http://link.springer.com/book/10.1007/978-3-540-30726-6|Book on spectral methods]]
Spectral Methods: Fundamentals in Single Domains
By Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

**NA** [[http://newdoc.nccu.edu.tw/teasyllabus/111648701013/Numerical_Analysis.pdf|An introduction to Numerical Analysis]], by Süli and Mayers.

**Handouts** See It's learning
==== Timetable ====

^ Week  ^ Date          ^ Literature  ^ Subject  ^                      
| 34    | 22.08, 24.08  |  Note by Krogstad and H.H Olsen | Meeting for organization of the course. The governing equations for incompressible fluid flow and coupled fluid/thermal problems. Introduction to the course.     |  
| 35    | 30.08, 31.08  |SM and NA  |Approximation and interpolation by high order polynomials. The Poisson problem: finite element and spectral discretizations in 1D.                                                                                                                                                             |   
| 36    | 06.09, 07.09  |           |The Poisson problem: spectral element discretization in 1D. The Poisson problem: spectral discretization in 2D (and 3D).                                                                                                                                                            |   
| 37    | 13.09, 14.09  |           | Programming exercises                                                                                                                                       |   
| 38    | 20.09, 21.09  |           | Guest Lecture                                                                                                                                               | 
| 39    | 27.09, 28.09  |           | Local and global data representations; tensor-product forms; fast diagonalization methods. Spectral methods in deformed geometries; isoparametric mapping.                         |                                                                                                                                 |   |
| 40    | 04.10, 05.10  |           | Deformed geometries; the Gordon-Hall algorithm.  The Poisson problem: general mixed Neumann/Dirichlet boundary conditions along curved boundaries.                                |                                                     |   |
| 41    | 11.10, 12.10  |           | The steady Stokes problem: indroduction. Symmetric saddle problems: the Uzawa algorithm; Lagrange multipliers.  |                                                                                                                                                         |   |
| 42    | 18.10, 19.10  |           | Symmetric saddle problems: uniqueness; the inf-sup condition. The steady Stokes problem: uniqueness; the Uzawa algorithm; the P_N-P_{N-2} method. |   
| 43    | 24.10, 25.10         |           | Guest lecture. The steady Stokes problem: the P_N-P_{N-2} method; the stress formulation.  Steady convection problems: steady convection-diffusion; steady Navier-Stokes.                                                                                                                                     |   
| 44    | 01.11, 02.11  |           | Time-dependent problems; ODE solvers; single operator treatment. The time-dependent Navier-Stokes equations; operator splitting methods.                                                                                                                                                           |   
| 45    | 08.11, 09.11  |           | The time-dependent Navier-Stokes equations: a convection-Stokes splitting scheme. The time-dependent Navier-Stokes equations: a pressure-velocity splitting scheme.                                                                                                                                                         |   
| 46    | 15.11         |           | The time-dependent Navier-Stokes equations (summary); computation of basic spectral tools (points, weights, basis, etc). Time-dependent convection problems; numerical dispersion.                                                                                                                                                           |   
| 47    | 22.11, 23.11  |           |                                                                                                                                                             |