Numerical Methods for Partial Differential Equations

Ferienpräsenz: we offer consultation hours during the semester break where you can ask question about the lecture material. For the dates see  this document (in German). It also lists the dates for the Prüfungseinsicht.

Lecturer: Ralf Hiptmair

Assistants: Eivind Fonn, Holger Brandsmeier, Axel Obermeier, Laura Scarabosio

Lecture hours:

• Monday, 15-17, HG E 7
• Friday, 08-10, HG E 3

Exercise classes:

• CSE: Wednesday, 08-10, ML F 40
  
• INFK: Wednesday, 13-15, HG F 26.5
• INFK: Thursday, 13-15, HG E 41
  

Consultation hours:

• Friday, 12-13: HG J 46 (Holger Brandsmeier)
• Monday, 11-12: HG J 59 (Eivind Fonn)
• Monday, 12-13: HG J 46 (Laura Scarabosio)
• Monday, 14-15: HG J 45 (Axel Obermeier)
  

Students not from RW/CSE, please choose an exercise class here. (Will be online in the first week of the semester.)

Assignments

There will be 12 weekly assignments handed out every Monday (first time on February 22nd). They should be handed in the following week before midnight on Monday in the labeled box at HG G 53.X.

Exercises will yield a certian number of points and will also be marked as either core or non-core. Core exercises (about two per week) indicate a higher degree of relevance to the final examination.

Testat requirements:

• Testat is given for achieving an equivalent of 90% of the total points of all core exercises.
• The testat is not required for taking the final exam, but it does count for 10% of the final grade.

For submitting your MATLAB code, please use the online submission interface.

Assignments, lecture nots and other handouts

Examination

The examination will be computer-based, with both programming and theoretical exercises. More info to come as the date draws nearer.

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 algorithm.
• understand research publications on theoretical and practical aspects of numerical methods for partial differential equations.

Programming Language: All implementations will be done in MATLAB.

Content of the course

• The finite element method (FEM)
• Special elliptic boundary value problems
• Parabolic boundary value problems
• Numerical methods for conservation laws

See a more comprehensive list on the VVZ.

Matlab links

Students of ETH can download Matlab via Stud-IDES for free (product name 'Matlab free').

• Matlab online documentation from MathWorks
• Matlab primer

Literature

This list should be interpreted as supplementary reading beyond the lecture notes, and is neither important nor required for following the course.

• D. Braess, Finite Elements, 2nd Edition, Cambridge University Press, 2001.
• 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.
• R. LeVeque, Finite Volume Methods for Hyperbolic Problems, Cambridge University Press, 2002.
• W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations, Lectures in Mathematics, ETH Zürich, Birkhäuser, 2003.
• A. Quarteroni, R. Sacco und F. Salieri, Numerische Mathematik, Springer, 2002.

Further literature

These are beyond the scope of this course, and are listed htere 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.