Numerical Methods for Elliptic and Parabolic PDEs
General informations
- Lecture informations available on the vvz website
- Lecture notes will be handed on hard copy
Lectures
| First lecture |
20.09.2016 |
| Tuesday |
15:15-17:00 (HG E 33.1) |
| Thursday |
13:15-15:00 (HG D 7.2) |
Exercise sessions
| First session |
26.09.2016 |
| Monday |
17:15-18:00 (HG E 21) |
| Assistants |
Fernando Henriquez and Denis Devaud |
| Office hours |
preferably by appointment (e-mail) |
| Hand in |
in the exercise class or in the marked box in front of HG G 53.x before the next exercise session (if possible, please also provide a printout of your code) |
Submission of programming problems (Matlab) can be done here.
As testate conditions are not in place anymore, it is not compulsory, yet recommended, to hand in the exercises for correction.
Assignments are published on Thursdays.
Assignments
Exam
Please find all necessary information here.
Aims of the course
This course gives a comprehensive introduction into the numerical treatment of linear and non-linear elliptic boundary value problems, related eigenvalue problems and linear, parabolic evolution problems.
Emphasis is on theory and the foundations of numerical methods.
Practical exercises include MATLAB implementations of finite element methods.
Participants of the course should become familiar with
- Concepts underlying the discretization of elliptic and parabolic boundary value problems
- Analytical techniques for investigating the convergence of numerical methods for the approximate solution of boundary value problems
- Methods for the efficient solution of discrete boundary value problems
- Implementational aspects of the finite element method
Content of the course (cf. )
- Elliptic boundary value problems
- Galerkin discretization of linear variational problems
- The primal finite element method
- Mixed finite element methods
- Discontinuous Galerkin Methods
- Boundary element methods
- Spectral methods
- Adaptive finite element schemes
- Singularly perturbed problems
- Sparse grids
- Galerkin discretization of elliptic eigenproblems
- Non-linear elliptic boundary value problems
- Discretization of parabolic initial boundary value problems
Literature
Main references
- S.C. Brenner and L. Ridgway Scott, The mathematical theory of Finite Element Methods, New York, Berlin, Springer, cop.1994. (online PDF)
- A. Ern and J.L. Guermond, Theory and Practice of Finite Element Methods, Springer Applied Mathematical Sciences Vol. 159, Springer, 1st Ed. 2004. (online PDF)
- R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods, Oxford University Press, 2013. (Chapter 1)
Additional literature
- D. Braess, Finite Elements, Cambridge Univ. Press, 3rd Ed. 2007. (Also available in German)
- D.A. Di Pietro and A. Ern, Mathematical Aspects of Discontinuous Galerkin Methods, Springer, vol. 69 SMAI Mathématiques et Applications, 2012. (online PDF)
- V. Thomée, Galerkin Finite Element Methods for Parabolic Problems, Springer Verlag, 2nd Ed. 2006. (online PDF)
Note: "online PDF" applies to users in the ETH domain (student computers / ETH WiFi / VPN)
Matlab links
ETH students can download Matlab with a free network license from the IT-Shop .
Matlab tutorials