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


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
2016-10-24, Elena Celledoni