MM839: Numerical analysis of hyperbolic conservation laws

Study Board of Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310062102
Assessment: Second examiner: None
Grading: Pass/Fail
Offered in: Odense
Offered in: Spring
Level: Master's level course approved as PhD course

STADS ID (UVA): N310062101
ECTS value: 10

Date of Approval: 01-11-2022

Duration: 1 semester

Version: Approved - active

Entry requirements

A Bachelor’s degree in pure or applied mathematics, computer science or physics.
You can not sign up for MM839 if you follow or have passed MM527.

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. 


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 


See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)




Mandatory assignments with oral presentation




Second examiner: None




Student Identification Card


Normally, the same as teaching language

Examination aids

To be announced during the course.

ECTS value


Indicative number of lessons

74 hours per semester

Teaching Method

The teaching method is based on three phase model.
  • 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.

Activities during the study phase:
  • self-study
  • problem solving

Teacher responsible

Name E-mail Department
Achim Schroll Computational Science


Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Educational Law & Registration


Offered in


Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.