MM839: Numerical analysis of hyperbolic conservation laws
You can not sign up for MM839 if you follow or have passed MM527.
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
- 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
- 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.
- 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
Exam element a)
Mandatory assignments with oral presentation
To be announced during the course.
Indicative number of lessons
- Intro phase: 48 hours
- Skills training phase: 24 hours, hereof tutorials: 24 hours
The intro phase consists of lectures where concepts, theories, models and ideas are introduced. The instructor activates the students through varied and flexible communication. In the training phase, students translate the academic knowledge into skills, test the skills and immerse oneself into the material.
- problem solving
|Achim Schrollemail@example.com||Institut for Matematik og Datalogi, Anvendt Matematik|