Coursebooks

Numerical approximation of PDE's II

Picasso Marco

English

Summary

A priori and a posteriori error estimates of numerical methods for elliptic, parabolic and hyperbolic pdes. Adaptive algorithms.

Content

• Elliptic pdes with finite elements:

- Diffusion problems: a posteriori error estimates in the natural H1 norm, in the L2 norm, goal oriented, adaptive algorithms.

- Extensions to Stokes problem, optimal control and nonlinear problems.

• Parabolic pdes:

- The heat equation: functional setting, space and time discretization, a posteriori error estimates, adaptive algorithms.

- Extension to nonlinear problems.

• Hyperbolic pdes: space discretization, a posteriori error estimates for the transport equation and the wave equation.

Learning Prerequisites

Recommended courses

Analysis I and II, Numerical analysis, Introduction to the finite elements methods, Numerical approximation of partial differential equations I

Learning Outcomes

By the end of the course, the student must be able to:
• Expound the methods presented during the course and exercices
• Implement these methods in specific examples

Teaching methods

Ex cathedra lecture and exercises in the classroom

Assessment methods

Oral exam

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.

In the programs

• Applied Mathematics, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Applied Mathematics, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics - master program, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Mathematics for teaching, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Computational science and Engineering, 2018-2019, Master semester 1
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• Lecture
2 Hour(s) per week x 14 weeks
• Exercises
2 Hour(s) per week x 14 weeks
• Computational science and Engineering, 2018-2019, Master semester 3
• Semester
Fall
• Exam form
Oral
• Credits
5
• Subject examined
Numerical approximation of PDE's II
• 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
14-15
15-16
16-17
17-18
18-19
19-20
20-21
21-22
Under construction
Lecture
Exercise, TP
Project, other

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• Autumn semester
• Winter sessions
• Spring semester
• Summer sessions
• Lecture in French
• Lecture in English
• Lecture in German