Lecture and recitations:

Numerical Methods for Partial Differential Equations II

summer term 2025

lecturer: Prof. Dr. Benedikt Wirth
recitations: tba

Information on the lecture

Learnweb: In the Learnweb you find the course under the name "Numerik Partieller Differentialgleichungen II SoSe 2025, 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. 10:15 to 11:45, weekly, M 3
Th. 10:15 to 11:45, weekly, M 3
different time in first week: online lecture We, April 9, 10-12 (see learnweb)
contents: The lecture covers advanced topics in the field of numerics for PDEs; potential content I have in my mind includes finite element numerics for mathematical elasticity, finite volume methods, methods for fluid dynamics, infinite-dimensional Hamiltonian systems, or ML-approximations of high-dimensional phase field equations. Below we will list the topics treated in the lectures.
enrolment: Please do not forget the compulsory enrolment in QISPOS.
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 up to one week before the exam. If you cannot enrol via QISPOS, please notify the lecturer.
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

Homework: Depending on the number of participants, instead of handing in homework each week we might have each participant present the homework solutions from time to time - the procedure will be decided on during the first two weeks of the term.
Information on the homework will be posted in the learnweb course of the lecture.
time, location: Fr. 10:00 to 12:00, SR 1B

begin of recitations: April 25, 2025