Numerical Methods for Partial Differential Equations | last update: 2021-10-03 |
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Lecture | up |
Numerical Methods for Partial Differential Equations - Lectures
(CourseId 327.320, 4 hours per week, Semester 5)Lecturer: O.Univ.-Prof. Dr. Ulrich Langer
Time and room:
| Wed, Oct 4, 2006 | 08:30 - 10:00 Room: HF 9901 | Lecture 1 |
| Thu, Oct 5, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 2 |
| Mon, Oct 9, 2006 | 10:15 - 11:45 Room: T 041 | Lecture 3 |
| Wed, Oct 11, 2006 | 08:30 - 10:00 Room: HF 9901 | Lecture 4 |
| Thu, Oct 12, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 5 |
| Wed, Oct 18, 2006 | 08:30 - 10:00 Room: HF 9901 | Lecture 6 |
| Thu, Oct 19, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 7 |
| Wed, Oct 25, 2006 | 08:30 - 10:00 Room: HF 9901 | Lecture 8 |
| Thu, Oct 26, 2006 | national holiday | Lecture is cancelled |
| Mon, Oct 30, 2006 | 10:15 - 11:45 Room: T 041 | Lecture 9 |
| Wed, Nov 1, 2006 | Allerheiligen (religious holiday) | Lecture is cancelled |
| Thu, Nov 2, 2006 | Allerseelen (religious holiday) | Lecture is cancelled |
| Wed, Nov 8, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 10 |
| Thu, Nov 9, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 11 |
| Wed, Nov 15, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 12 |
| Thu, Nov 16, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 13 |
| Wed, Nov 22, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 14 |
| Thu, Nov 23, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 15 |
| Mon, Nov 27, 2006 | 13:45 - 15:15 Room: P 004 | Lecture 16 |
| Wed, Nov 29, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 17 |
| Wed, Dec 6, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 18 |
| Thu, Dec 7, 2006 | 08:30 - 10:00 Room: HS 13 | Lecture 19 |
| Mon, Dec 11, 2006 | 13:45 - 15:15 Room: P 004 | Lecture 20 |
| Wed, Dec 13, 2006 | 08:30 - 10:00 Room: K 034D | Lecture 21 |
| Wed, Jan 10, 2007 | 08:30 - 10:00 Room: K 034D | Lecture 22 |
| Thu, Jan 11, 2007 | 08:30 - 10:00 Room: HS 13 | Lecture 23 |
| Wed, Jan 17, 2007 | 08:30 - 10:00 Room: K 034D | Lecture 24 |
| Thu, Jan 18, 2007 | 08:30 - 10:00 Room: HS 13 | Lecture 25 |
| Wed, Jan 24, 2007 | 08:30 - 10:00 Room: K 034D | Lecture 26 |
| Thu, Jan 25, 2007 | 08:30 - 10:00 Room: HS 13 | Lecture 27 |
| Wed, Jan 31, 2007 | 08:30 - 10:00 Room: K 034D | Lecture 28 |
Lecturer: O.Univ.-Prof. Dr. Ulrich Langer
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Tutorial | up |
Numerical Methods for Partial Differential Equations - Tutorials
(CourseId 327.321, 2 hours per week, Semester 6)Tutorials held by: Dr. Marco Discacciati
Time and room:
| Mon, Oct 16, 2006 | 10:15 - 11:45 Room: T 041 | Tutorial 01 |
| Mon, Oct 23, 2006 | 10:15 - 11:45 Room: T 041 | Tutorial 02 |
| Mon, Nov 6, 2006 | 13:45 - 15:15 Room: P 004 | Tutorial 03 |
| Mon, Nov 13, 2006 | 13:45 - 15:15 Room: P 004 | Tutorial 04 |
| Mon, Nov 20, 2006 | 13:45 - 15:15 Room: P 004 | Tutorial 05 |
| Thu, Nov 30, 2006 | 08:30 - 10:00 Room: HS 13 | Tutorial 06 |
| Mon, Dec 4, 2006 | 13:45 - 15:15 Room: P 004 | Tutorial 07 |
| Thu, Dec 14, 2006 | 08:30 - 10:00 Room: HS 13 | Tutorial 08 |
| Mon, Jan 8, 2007 | 13:45 - 15:15 Room: P 004 | Tutorial 9 |
| Mon, Jan 15, 2007 | 13:45 - 15:15 Room: P 004 | Consultation |
| Mon, Jan 22, 2007 | 13:45 - 15:15 Room: P 004 | Tutorial 10 |
| Mon, Jan 29, 2007 | 13:45 - 15:15 Room: P 004 | Tutorial 11 |
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Exercises | up |
| Exercise 1 | October 16, 2006 | ||
| Exercise 2 | October 23, 2006 | solution(pdf) | |
| Exercise 3 | November 6, 2006 | ||
| Exercise 4 | November 13, 2006 | ||
| Exercise 5 | November 20, 2006 | ||
| Exercise 6 | November 30, 2006 | ||
| Exercise 7 | December 4, 2006 | ||
| Exercise 8 | December 14, 2006 | tex-file | |
| Exercise 9 | January 8, 2007 | ||
| Exercise 10 | January 22, 2007 | ||
| Exercise 11 | January 29, 2007 | ||
| Exercise 1-2,8 | tex-files | zip |
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Transparencies | up |
| Transparency 1: colour | Galerkin-Ritz |
| Transparency 2: colour | Assembling Algorithm |
| Transparency 3: colour | 1.4.4. FEM for PDEs |
| 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 7: colour | Example 1.34 |
| Transparency 8: b/w | 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: colour | exRKF: Consistency |
| Transparency 18: colour | Example 2.15 |
| Transparency 19: b/w | Example 2.16 |
| Transparency 20: colour | Remark 2.17 |
| Transparency 21: colour | Remark 2.17 (cont.) |
| Transparency 22: colour | Remark 2.19 |
| Transparency 23: colour | Example 2.20 |
| Transparency 24: b/w | 2.3.7. Stability Analysis I |
| Transparency 25: b/w | 2.3.7. Stability Analysis II |
| Transparency 26: colour | 2.3.7. Stability Analysis III |
| Transparency 27: colour | 2.3.7. Stability Analysis IV |
| Transparency 28: colour | 2.4. Full Discretization |
| Transparency 29: b/w | 3.1. Hyperbolic PDE I |
| Transparency 30: colour | 3.1. Hyperbolic PDE II |
| Transparency 31: colour | 3.1. Hyperbolic PDE III |
| Transparency 32: colour | 3.1. Hyperbolic PDE IV |
| Transparency 33: colour | 3.2. RKM I |
| Transparency 34: colour | 3.2. RKM II |
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Basic Lecture Notes: | up |
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).
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Additional Literature: | up |
[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.
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Software: | up |
| FEM1D |
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Links: | up |
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General Information | up |
- Linear Algebra and Analytic Geometry 1 and 2
- Analysis 1 - 3 (particularly Analysis 3)
- Knowledge of Computer Science and Programming
- Numerical Analysis
- Partial Differential Equations and Integral Equations
- Numerical Methods for Elliptic Partial Differential Equations
- Numerical Methods for Non-Stationary Problems
- Special Topics in Computational Mathematics
- Special Seminars in Computational Mathematics
Get knowledge of analysis tools and for the numerical methods for the solution of partial differential equations (PDEs.)
Contents:
Numerical Methods for
- Elliptic Partial Differential Equations
- Parabolic Partial Differential Equations
- Hyperbolic Partial Differential Equations
- The tutorial to this lecture treats numerical methods for the solution of PDEs and has 2 hours per week
- First Tutorial: Thursday, October 12, 2006, 08:30 - 10:00, Lecture Room HS 13
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.
