Lecture and recitations:

Numerische Methoden für partielle Differentialgleichungen I

winter term 2026/27

lecturer: Prof. Dr. Benedikt Wirth
recitations: tba

Information on the lecture

Learnweb: In the Learnweb you find the course under the name "Numerics for Partial Differential Equations WiSe 2026/27, Benedikt Wirth". Please enrol into that course if you intend to attend the lecture. Any information about the lecture, the homework etc. can be found there.
time, location: Mo. 12 ct, weekly, M 4
Th. 12 ct, weekly, M 4
start of the lecture: October 12, 2026
contents: Students will learn how to solve partial differential equations numerically and how to analyse the corresponding methods. Topics include
  • spatial discretization methods (finite differences, finite elements) for elliptic boundary value problems
  • time- and space discretization methods for parabolic and hyperbolic evolution equations
  • stability concepts
  • convergence analysis
  • error estimates
enrolment: Please do not forget the compulsory enrolment in QISPOS/SLcM.
assessment: To pass the course you will have to achieve a 50 % score in the homework and pass the half-hour oral or three-hour written exam at the end of the course (to be admitted to the exam, the 50 % score is mandatory). The type of exam will be announced in the lecture and will depend on the number of participants.

Note that there might be a few examination regulations which do not require a half-hour oral or three-hour written exam (but rather a two-hour exam or no exam at all). If you are studying according to such examination regulations, please notify the lecturer at the beginning of term. A 50 % homework score will be required in all cases.

One can usually enrol for the exam in QISPOS/SLcM up to one week before the exam. If you cannot enrol via QISPOS/SLcM, please notify the lecturer.
material: lecture notes
literature:
  • D. Braess. Finite Elemente. Springer, Berlin, 1997. (English version)
  • L.N. Trefethen. Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations
  • P.G. Ciarlet. The Finite element method for elliptic problems. North-Holland, Amsterdam, 1987.
  • Hans Wilhelm Alt. Lineare Funktionalanalysis. Eine anwendungsorientierte Einführung. Hochschultext. Berlin etc.: Springer-Verlag., 1992
  • Walter Rudin. Functional Analysis. McGraw-Hill 1991.
  • Christian Grossmann and Hans-Georg Roos. Numerik partieller Differentialgleichungen. Teubner Studienucher Mathematik. [Teubner Mathematical Textbooks]. B. G. Teubner, Stuttgart, second edition, 1994.
  • L. C. Evans: Partial Differential Equations, AMS, 2010.
  • F. John: Partial Differential Equations , Springer, 1981, 1991 (Reprint).
  • Wolfgang Hackbusch. Theorie und Numerik elliptischer Differentialgleichungen. Teubner Studienbücher Mathematik. [Teubner Mathematical Textbooks]. B. G. Teubner, Stuttgart, second edition, 1996
  • W. Hackbusch: Iterative Lösung großer schwach besetzter Gleichungssysteme. Leitfäden der Angewandten Mathematik und Mechanik, 69. Teubner Studienbücher Mathematik. Teubner, Stuttgart, 1991.
  • G. Dziuk: Theorie und Numerik partieller Differentialgleichungen, De Gruyter, Berlin/New York, 2010.
  • S.C. Brenner, L.R. Scott: The mathematical theory of finite element methods, Springer, New York/Berlin, 2002.
  • Yousef Saad. Iterative methods for sparse linear systems. Society for Industrial and Applied Mathematics, Philadelphia, PA, second edition, 2003.
  • Hans-Rudolf Schwarz. Methode der Finiten Elemente, volume 47 of Leitaden der Angewandten Mathematik und Mechanik [Guides to Applied Mathematics and Mechanics]. B. G. Teubner, Stuttgart, third edition, 1991. Eine Einführung unter besonderer Berücksichtigung der Rechenpraxis. [An introduction with special reference to computational practice], Teubner Studienbücher Mathematik. [Teubner Mathematical Textbooks].
  • online-book: S. Larsson, V. Thomee: Partielle Differentialgleichungen und numerische Methoden (English version)
  • online-book: Manfred Dobrowolski: Angewandte Funktionalanalysis
  • E. Süli: Numerical solution of partial differential equations. (brief introduction into the topic with further reading list)

Information on the tutorials

Learnweb: Same as for lecture. Information on the homework will be posted there.
time, location: Fr. 10:00 to 12:00, room tba

begin of recitations: October 23, 2026