Numerical Methods for Partial Differential Equations
Please note that this page is old.
Check in the VVZ
for a current information.
Lecturer: Ralf Hiptmair
Head Assistants: Roger Käppeli, Kjetil Lye, Carolina Urzúa Torres.
Assistants: Laura Scarabosio, Elke Spindler.
- Monday, 15-17, HG F 1
- Tuesday, 15-17, HG F 1
There will be assignment every week. TBA.
Testat requirements: NONE.
For submitting your code, please use the online submission interface and choose the course n. 5.
Assignments, lecture notes and other handouts
3 hour computer-based examination, with both programming and theoretical exercises. Parts of the lecture slides, C++ documents, and Eigen documentation will be made available during the examination. More info to come as the date draws nearer.
Midterm and endterm exams:
1. Midterm on April 12, 15:30 - 16:00
2. Endterm on May 24, 15:15 - 15:45
Term exams last 30 minutes, closed book, achieving 100% of the points in a term exam will yield a BONUS of 10% of the points for the session exam. Passing of either term exam is not required for admission to the session exam. Repetition of term exams is not possible.
Aims of the course
Introduce students of Applied Mathematics, Computational Science and Engineering and Computer Science to the most widely used numerical solution methods for ordinary and partial differential equations, their mathematical properties, and their computer implementation.
Students should be able to:
- implement advanced numerical methods for the solution of partial differential equations efficiently.
- modify and adapt numerical algorithms guided by awareness of their mathematical foundations.
- select and assess numerical methods in light of the predictions of theory.
- identify features of a PDE (= partial differential equation) based model
that are relevant for the selection and performance of a numerical
- understand research publications on theoretical and practical aspects of numerical methods for partial differential equations.
Programming Language: implementations will be done in C++.
Content of the course
- 2-point boundary value problems
- Elliptic boundary value problems
- Parabolic boundary value problems
- Hyperbolic problems
See a more comprehensive list on the VVZ.
Eigen documentation here
The codes for the exercises and lecture notes are available online:
Codes can be downloaded from the public git repository.
This list should be interpreted as supplementary reading beyond the lecture notes, and is neither important nor required for following the course.
- W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2003.
- D. Braess, Finite Elements, 2nd Edition, Cambridge University Press, 2001.
- S. Brenner and R. Scott, Mathematical theory of finite element methods, Texts in Applied Mathematics. Springer–Verlag, New York, 1994.
- A. Ern and J.-L. Guermond Theory and Practice of Finite Elements, volume 159 of Applied Mathematical Sciences. Springer, New York, 2004.
- Ch. Großmann and H.-G. Roos, Numerik partieller Differentialgleichungen, Teubner Studienbücher Mathematik. Teubner, Stuttgart, 1992.
- W. Hackbusch, Elliptic Differential Equations. Theory and Numerical Treatment, volume 18 of Springer Series in Computational Mathematics. Springer, Berlin, 1992.
- T. Hughes, The Finite Element Method, Dover Publications, 2000.
- C. Johnson, Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge University Press, 1987.
- P. Knabner and L. Angermann, Numerical Methods for Elliptic and Parabolic Partial Differential Equations, volume 44 of Texts in Applied Mathematics. Springer, Heidelberg, 2003.
- S. Larsson and V. Thomée, Partial Differential Equations with Numerical Methods, volume 45 of Texts in Applied Mathematics. Springer, Heidelberg, 2003.
- R. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.
- A. Quarteroni, R. Sacco und F. Salieri, Numerische Mathematik, Springer, 2002.
These are beyond the scope of this course, and are listed here for the particularly interested.
- C. Canuto, M.Y. Hussaini, A. Quarteroni und T.A. Zang, Spectral Methods, Springer, 2006.
- M. Feistauer, J. Felcman, and I. Straskraba, Mathematical and Computational Methods for Compressible Flow, Oxford: Clarendon Press, 2003.
- A. Tveito und R. Winther, Einführung in Partielle Differentialgleichungen, Springer, 2002.