English

MM839: Numerical analysis of hyperbolic conservation laws (10 ECTS)

STADS: 13016401

Level
Master's level course approved as PhD course

Teaching period
The course is offered in the spring semester.

Teacher responsible

Email: achim@imada.sdu.dk

Timetable

Group	Type	Day	Time	Classroom	Weeks
Common	I	Monday	10-12	U146	6-7,13
Common	I	Monday	10-12	U147	8-9
Common	I	Monday	10-12	U151	10
Common	I	Monday	10-12	U145	11,14,18-19
Common	I	Monday	10-12	IMADA semi	12,17
Common	I	Wednesday	08-10	U146	5
Common	I	Thursday	16-18	IMADA semi	5-12,14,17-18
Common	I	Thursday	16-18	U142	13
H1	TE	Wednesday	08-10	U17	6-10
H1	TE	Wednesday	08-10	IMADA semi	11,13-14
H1	TE	Wednesday	12-14	IMADA semi	12
H1	TE	Wednesday	08-10	U156	12
H1	TE	Wednesday	08-10	U141	17-18
H1	TE	Thursday	16-18	IMADA semi	19

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Comment:
Ubegrænset deltagerantal.

samlæst med MM527

Prerequisites:
A Bachelor’s degree in pure or applied mathematics, computer science or physics.

Academic preconditions:

Students taking the course are expected to:

Have knowledge of calculus, linear algebra, numerical analysis and ordinary differential equations.
Be able to use some programming language, f.ex. Matlab

Course introduction

The aim of the course is to enable the student by analytic and numerical methods to solve problems in natural science, which is important in regard to write a master thesis and to work in natural science.

The course builds on the knowledge acquired in the courses MM547, and gives an academic basis to write a master thesis, that are part of the degree.

In relation to the competence profile of the degree it is the explicit focus of the course to:

Give the competence to perform scientific projects, to participate in interdisciplinary collaboration and to take responsibility for own learning and specialization.
Give skills in problem solving, analytic thinking and scientific communication.
Give knowledge and understanding of advanced models and methods in applied mathematics, including some from the research frontier of the field, as well as knowledge of the application of these models and methods to problems pertaining to other scientific areas and to the business world.

Expected learning outcome

The learning objective of the course is that the student demonstrates the ability to:

formulate conservation laws in integral and differential form.
explain the Kruzkov entropy solution.
describe with the issues that arise when computing weak solutions like contact discontinuities and shock waves.
construct exact and approximate solutions to Riemann problems.
Explain conditions for stability of numerical methods.
implement modern high resolution algorithms in one space dimension.

Subject overview

The following main topics are contained in the course:

Conservation laws as integral and partial differential equations.
Shock formation, weak solutions and entropy conditions.
The Kruzkov entropy solution.
Finite Volume methods and the Riemann Problem.
Stability analysis of numerical methods
Godunov-, upwind-, and Lax-Friedrichs methods.
High resolution methods

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

Expected working hours
The teaching method is based on three phase model.
Intro phase: 50 hours
Skills training phase: 24 hours, hereof:
- Tutorials: 24 hours

Educational activities

- self-study
- problem solving

Educational form

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.