MATH-459 / 5 crédits

Enseignant: Licht Martin Werner

Langue: Anglais

## 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.

## Keywords

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

## 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

By the end of the course, the student must be able to:

• 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 2 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 30% 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.

## Bibliography

The class will use the text

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

## Dans les plans d'études

• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines
• Semestre: Automne
• Forme de l'examen: Oral (session d'hiver)
• Matière examinée: Numerical methods for conservation laws
• Cours: 2 Heure(s) hebdo x 14 semaines
• Exercices: 2 Heure(s) hebdo x 14 semaines

## Semaine de référence

 Lu Ma Me Je Ve 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 19-20 20-21 21-22

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