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MAI0106 Lecture content

Lecture 1

Introduction. General principles and ideas.

Notes here.

Lecture 2-3

Periodic solutions and Fourier analysis. The Petrovski condition for PDE and the von Neumann condition for difference schemes. (Sec. 2.1-2.2)

Notes on the continuous problem here, notes on the discrete problem here.

Lecture 4-6

The energy method. Semi-bounded operators. Symmetric and skewsymmetric operators. (Sec. 2.3)

Notes for lecture 4,5,6 follows here, here and here.

Lecture 7-9

Normal mode analysis. The Kreiss condition. (Sec. 2.4 + Handouts)

Lecture 10

Well-posed boundary conditions in practise. Handouts-1, Handouts-2, Handouts-3

Lecture 11

The error equation. Energy estimates. Accuracy of discrete approximation. Unceartainty in data. Initial and boundary conditions. (Sec. 3.1-3.2 + Handouts)

Lecture 12

Effectiveness of high order schemes. (Sec. 1.1-1.2)

Lecture 13

Approximation in space. Standard and staggered grids. Pade type difference operators. (Sec. 4.1-4.3)

Lecture 14

Approximation in time. The test equation. Runge-Kutta and linear multi-step methods. The Lax-Wendroff principle.(Sec 5.1-5.3,6.1)

Lecture 15-16

Boundary treatment. Summation by parts (SBP) operators. Weak boundary conditions. Strict/time stability. (Sec. 7.1-7.4 + Handouts_1 + Handouts_2)

Lecture 17-18

Structured multi-block methods. Unstructured finite volume methods and discontinuous Galerkin methods. Stability and conservation. (Sec. 12.2 + Handouts_1 + Handouts_2 + Handouts_3 + Handouts_4)

Related Material

A lecture schedule for CME326 is given here.

Sidansvarig: jan.nordstrom@liu.se
Senast uppdaterad: 2019-11-29