Conservation Methods for Hyperbolic Differential Equations
Postgraduate course
- ECTS credits
- 10
- Teaching semesters Autumn
- Course code
- MAT361
- Number of semesters
- 1
- Teaching language
- English
- Resources
- Schedule
Course description
Objectives and Content
The course gives an introduction to hyperbolic conservation laws and to numerical methods for solving the equations. In the analytic part of the course one considers both for scalar equations and for a system of equations, topics as waves, entropy conditions and the solution of the Riemann problem. In the numerical part of the course one discusses topics as conservation, monotony, stability and accuracy of methods used.
Learning Outcomes
By the end of the course, students should be able to:
- Analyze scalar and systems of hyperbolic conservation laws and understand their weak solutions.
- Explain the Rankine-Hugoniot jump condition and Olenik's entropy conditions.
- Describe the solution of the Riemann problem for both scalar and selected system of hyperbolic equations
- Explain the importance of conservation and monotonicity for numerical methods for hyperbolic equations.
- Evaluate and compare the accuracy, stability, and resolution of numerical schemes for hyperbolic PDEs.
- Solve hyperbolic equations using Godunov, Engquist-Osher, and Lax-Friedrichs schemes.
The course is suitable for Master's- and Ph.D students
Semester of Instruction
Irregular, course will be offered if it is on this course list: Workbook: Emneliste for innreisende utvekslingsstudenter (uhad.no)
Required Previous Knowledge
None
Recommended Previous Knowledge
Compulsory Assignments and Attendance
Excercises
Forms of Assessment
Oral examination
Grading Scale
The grading scale used is A to F. Grade A is the highest passing grade in the grading scale, grade F is a fail.