MATH-459 / 5 credits

Teacher: Licht Martin Werner

Language: English


Summary

Introduction to the development, analysis, and application of computational methods for solving conservation laws with an emphasis on finite volume, limiter based schemes, high-order essentially non-oscillatory schemes, and discontinuous Galerkin methods.

Content

Keywords

Conservation laws, finite volume methods, MUSCL scheme, ENO/WENO methods, discontinuous Galerkin methods

Learning Prerequisites

Required courses

A course in partial differential equations and their numerical approximation. Knowledge of finite difference methods.

Important concepts to start the course

Linear partial differential equations, numerical approximation, stability, convergence. Basic methods for solving ordinary differential equations and computational linear algebra.

Learning Outcomes

  • Choose an appropriate method
  • Analyze methods
  • Assess / Evaluate computational methods
  • Carry out computational experiments
  • Carry out mathematical analysis
  • Construct computational methods
  • Prove basic mathematical properties

Transversal skills

  • Assess progress against the plan, and adapt the plan as appropriate.
  • Set objectives and design an action plan to reach those objectives.
  • Continue to work through difficulties or initial failure to find optimal solutions.
  • Take feedback (critique) and respond in an appropriate manner.
  • Use both general and domain specific IT resources and tools
  • Access and evaluate appropriate sources of information.

Teaching methods

The class will be given as a lecture class with in-class computational experiments to support the analysis.

Expected student activities

Development of computational methods for conservation laws, their analysis, implementation and use for solving application examples of increasing complexity.

Assessment methods

There will be 3 required small reports to be handed in during the class. These will be examined as part of the final oral examination and will count for 50% of the overall grade.

Dans le cas de l’art. 3 al. 5 du Règlement de section, l’enseignant décide de la forme de l’examen qu’il communique aux étudiants concernés.

Resources

Bibliography

The class will use the text

J.S. Hesthaven, Numerical Methods for Conservation Laws: From Analysis to Algorithms. SIAM Publishing, 2017.

Ressources en bibliothèque

Moodle Link

In the programs

  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks
  • Semester: Fall
  • Exam form: Oral (winter session)
  • Subject examined: Numerical methods for conservation laws
  • Lecture: 2 Hour(s) per week x 14 weeks
  • Exercises: 2 Hour(s) per week x 14 weeks

Reference week

 MoTuWeThFr
8-9     
9-10     
10-11     
11-12     
12-13     
13-14  MAA331  
14-15    
15-16    MAA110
16-17    
17-18     
18-19     
19-20     
20-21     
21-22     

Wednesday, 13h - 15h: Lecture MAA331

Friday, 15h - 17h: Exercise, TP MAA110