## Literature

**SM** Book on spectral methods
Spectral Methods: Fundamentals in Single Domains
By Claudio Canuto,M. Yousuff Hussaini,Alfio Quarteroni,Thomas A. Zang

**NA** 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 |