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Numerical Methods for Partial Differential Equations

 last update: 2013-12-05
[ Lecture ]  [ Tutorial ]  [ Exercises ]   [ Transparencies ]  [ Lecture Notes ]   [ Additional literature ]   [ Software ]  [ Links ]  [ General ]   [ Home ]

Homepage: http://www.numa.uni-linz.ac.at/Teaching/LVA/2007w/NuPDE/


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Lecture      up

Numerical Methods for Partial Differential Equations - Lectures

(Course Id 327.320, 4 hours per week, Semester 5)

Lecturer: O.Univ.-Prof. Dr. Ulrich Langer

Time and room:

Wed, Oct 3, 200708:30 - 10:00 Room: T 911Lecture 1
Thu, Oct 4, 200708:30 - 10:00 Room: HS 14Lecture 2
Wed, Oct 10, 2007cancelled
Thu, Oct 11, 200708:30 - 10:00 Room: HS 14Lecture 3
Mon, Oct 15, 200710:15 - 11:00 Room: T 212Lecture 4
Wed, Oct 17, 200708:30 - 10:00 Room: T 911Lecture 5
Thu, Oct 18, 200708:30 - 10:00 Room: HS 14Lecture 6
Wed, Oct 24, 200708:30 - 10:00 Room: T 911Lecture 7
Thu, Oct 25, 200708:30 - 10:00 Room: HS 14Lecture 8
Wed, Oct 31, 200708:30 - 10:00 Room: T 911Lecture 9
Thu, Nov 1, 2007Allerheiligen (religious holiday)cancelled
Wed, Nov 7, 200708:30 - 10:00 Room: T 911Lecture 10
Thu, Nov 8, 200708:30 - 10:00 Room: HS 14Lecture 11
Wed, Nov 14, 200708:30 - 10:00 Room: T 911Lecture 12
Thu, Nov 15, 200708:30 - 10:00 Room: HS 14Lecture 13
Wed, Nov 21, 200708:30 - 10:00 Room: T 911Lecture 14
Thu, Nov 22, 200708:30 - 10:00 Room: HS 14Lecture 15
Wed, Nov 28, 200708:30 - 10:00 Room: T 911Lecture 16
Thu, Nov 29, 200708:30 - 10:00 Room: HS 14Lecture 17
Wed, Dec 5, 200708:30 - 10:00 Room: T 911Lecture 18
Thu, Dec 6, 200708:30 - 10:00 Room: HS 14Lecture 19
Wed, Dec 12, 200708:30 - 10:00 Room: T 911Lecture 20
Thu, Dec 13, 200708:30 - 10:00 Room: HS 14Lecture 21
Wed, Jan 9, 200808:30 - 10:00 Room: T 911Lecture 22
Thu, Jan 10, 200808:30 - 10:00 Room: HS 14Lecture 23
Wed, Jan 16, 200808:30 - 10:00 Room: T 911Lecture 24
Thu, Jan 17, 200808:30 - 10:00 Room: HS 14Lecture 25
Wed, Jan 23, 200808:30 - 10:00 Room: T 911Lecture 26
Thu, Jan 24, 200808:30 - 10:00 Room: HS 14Lecture 27
Wed, Jan 30, 200808:30 - 10:00 Room: T 911Lecture 28
Thu, Jan 31, 200808:30 - 10:00 Room: HS 14Lecture 29

Lecturer: O.Univ.-Prof. Dr. Ulrich Langer



tutorial
Tutorial      up

Numerical Methods for Partial Differential Equations - Tutorials

(Course Id 327.321, 2 hours per week, Semester 6)

Tutorials held by: DI Clemens Pechstein, KG 5th floor

Time and room:

Mon, Oct 15, 200710:15 - 11:45 Room: T 212Lecture
Mon, Oct 22, 200708:30 - 10:00 Room: T 212Tutorial 01
Mon, Oct 29, 200708:30 - 10:00 Room: T 212Tutorial 02
Mon, Nov 5, 2007 — Consulting
Mon, Nov 12, 200708:30 - 10:00 Room: T 212Tutorial 03
Mon, Nov 19, 200708:30 - 10:00 Room: T 212Tutorial 04
Mon, Nov 26, 200708:30 - 10:00 Room: T 212Tutorial 05
Mon, Dec 3, 200708:30 - 10:00 Room: T 212Tutorial 06
Mon, Dec 10, 200708:30 - 10:00 Room: T 212Tutorial 07
Mon, Jan 7, 200808:30 - 10:00 Room: T 212Tutorial 08
Mon, Jan 14, 200808:30 - 10:00 Room: T 212Tutorial 09
Mon, Jan 21, 200808:30 - 10:00 Room: T 212Tutorial 10
Mon, Jan 28, 200808:30 - 10:00 Room: T 212Tutorial 11

For the programming exercises you can consult Clemens Pechstein.

exercises
Exercises      up

Tutorial 01October 22, 2007pdf
Tutorial 02October 29, 2007pdf
Tutorial 03November 12, 2007pdf
Tutorial 04November 19, 2007pdf
Tutorial 05November 26, 2007pdf    richardson.hpp
Tutorial 06December 3, 2007pdf
Tutorial 07December 10, 2007pdf    cg.hpp
Tutorial 08January 7, 2007pdf
Tutorial 09January 14, 2007pdf
Tutorial 10January 21, 2007pdf (corrected)
Tutorial 11January 28, 2007pdf
tex-fileszip



transparencies
Transparencies      up

Transparency 1: colourGalerkin-Ritz
Transparency 2: colourAssembling Algorithm
Transparency 3: colour1.4.4. FEM for PDEs
Transparency 3a: colourAFEM
Transparency 4: b/w Symm. case: Th. 1.26
Transparency 5: b/w Symm. case: R. 1.27
Transparency 6: b/w Remark 1.28
Transparency 6a: colour Remark 1.33
Transparency 7: colourExample 1.34
Transparency 8a: colour PCG
Transparency 8b: colour Alg. 1.38: PCG
Transparency 9: b/w 1.6. - 1.8.
Transparency 10: b/w Lemma 2.5.
Transparency 11: b/w Lemma 2.6.
Transparency 12: b/w Existence
Transparency 13: b/w Theorem 2.7
Transparency 14: b/w Discr. Error I
Transparency 15: b/w Discr. Error II (Th. 2.10)
Transparency 16: b/w Discr. Error III
Transparency 17: colourexRKF: Consistency
Transparency 18: colourExample 2.15
Transparency 19: b/w Example 2.16
Transparency 20: colourRemark 2.17
Transparency 21: colourRemark 2.17 (cont.)
Transparency 22: colourRemark 2.19
Transparency 23: colourExample 2.20
Transparency 24: b/w 2.3.7. Stability Analysis I
Transparency 25: b/w 2.3.7. Stability Analysis II
Transparency 26: colour2.3.7. Stability Analysis III
Transparency 27: colour2.3.7. Stability Analysis IV
Transparency 28: colour2.4. Full Discretization
Transparency 29: b/w 3.1. Hyperbolic PDE I
Transparency 30: colour3.1. Hyperbolic PDE II
Transparency 31: colour3.1. Hyperbolic PDE III
Transparency 32: colour3.1. Hyperbolic PDE IV
Transparency 33: colour3.2. RKM I
Transparency 34: colour3.2. RKM II

literature
Basic Lecture Notes:      up
[1] Zulehner W.: Numerical Methods for Partial Differential Equations, JKU, Linz, Winter Semester 2005/06.
PDF-File
[2] Langer U.: Numerik I (Operatorgleichungen), JKU, Linz 1996 (Sobolev-Spaces and Tools).
Postscript-File
[3] Langer U.: Numerik II (Numerische Verfahren für Randwertaufgaben), JKU, Linz 1996 (FEM and FVM).
Postscript-File
[4] Jung M., Langer U.: Methode der finiten Elemente für Ingenieure. Teubner-Verlag, Stuttgart, Leipzig, Wiesbaden 2001 (practical aspects of the FEM).
Methode der Finiten Elemente für Ingenieure
[5] Steinbach O.: Lösungsverfahren für lineare Gleichungssysteme: Algorithmen und Anwendungen. Teubner-Verlag, Stuttgart, Leipzig, Wiesbaden 2005 (solvers for systems of algebraic equations).
[6] Zulehner W.: Numerische Mathematik - Eine Einführung anhand von Differentialgleichungsproblemen. Band 1: Stationäre Probleme. Birkhäuser, Basel 2008.


additional literature
Additional Literature:      up
[1] Braess D.: Finite Elemente. Springer Lehrbuch, Berlin, Heidelberg 1997.
Braess D.: Finite elements: Cambridge University Press, 2001.
[2] Großmann C., Roos H.-G.: Numerik partieller Differentialgleichungen. Teubner-Verlag, Stuttgart 1992.
[3] Heinrich B.: Finite Difference Methods on Irregular Networks. Akademie-Verlag, Berlin 1987.
[4] Knaber P., Angermann L.: Numerik partieller Differentialgleichungen. Eine anwendungsorientierte Einführung. Springer-Verlag, Berlin-Heidelberg 2000.
[5] Monk P.: Finite Element Methods for Maxwell's Equations. Oxford Science Publications, Oxford 2003.
[6] Schwarz H.R.: FORTRAN-Programme zur Methode der finiten Elemente. B.G. Teubner, Stuttgart, 1991.
[7] Schwarz H.R.: Methode der finiten Elemente. B.G. Teubner, Stuttgart, 1991.
[8] Verfürth R.: A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley - Teubner, 1996.
[9] Ciarlet P.G.: The finite element method for elliptic problems. Classics in Applied Mathematics (40), SIAM, Philadelphia PA, 2002.
[10] Hairer E., Nørsett S.P., Wanner G.: Solving Ordinary Differential Equations I. Nonstiff Problems. Second Revised Edition. Springer Series in Computational Mathematics (8), Springer-Verlag Berlin Heidelberg 1987, 1993.
[11] Hairer E., Wanner G.: Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems. Second Revised Edition. Springer Series in Computational Mathematics (14), Springer-Verlag Berlin Heidelberg 1991, 1996.


software
Software:      up
FEM1D


links
Links:      up


general
General Information      up
Previous Knowledge:
Is required for:
Objective:
Get knowledge of analysis tools and for the numerical methods for the solution of partial differential equations (PDEs.)

Contents:
Numerical Methods for Additional Information:
Examinations:
Lecture:
The lecture contains an oral examination.

Tutorial:
The mark of the tutorial consists of the assessment of the individual exercises, the presentations on the blackboard and a practical exercise.