Numerical Methods for Elliptic Partial Differential Equations

last update: 2021-10-03
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Lecture      up

Numerical Methods for Elliptic Partial Differential Equations - Lectures

(CourseId 327.003, 4 hours per week, Semester 6)

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

Time and room:

Wed, March 1, 200610:15 - 11:45 Room: T 111Lecture 1
Thu, March 2, 200610:15 - 11:45 Room: T 111Lecture 2
Tue, March 7, 200610:15 - 11:45 Room: T 1010Lecture 3
Wed, March 8, 200610:15 - 11:45 Room: T 111Lecture 4
Thu, March 9, 200610:15 - 11:45 Room: T 111Lecture 5
Tue, March 14, 200610:15 - 11:45 Room: T 1010Lecture 6
Thu, March 16, 200610:15 - 11:45 Room: T 111Lecture 7
Wed, March 22, 200610:15 - 11:45 Room: T 111Lecture 8
Thu, March 23, 200610:15 - 11:45 Room: T 111Lecture 9
Wed, March 29, 200610:15 - 11:45 Room: T 111Lecture 10
Thu, March 30, 200610:15 - 11:45 Room: T 111Lecture 11
Wed, April 5, 200610:15 - 11:45 Room: T 111Lecture 12
Thu, April 6, 200610:15 - 11:45 Room: T 111Lecture 13
Wed, April 26, 200610:15 - 11:45 Room: T 111Lecture 14
Thu, April 27, 200610:15 - 11:45 Room: T 111Lecture 15
Tue, May 2, 200610:15 - 11:45 Room: T 1010Lecture 16
Wed, May 3, 200610:15 - 11:45 Room: T 111Lecture 17
Thu, May 4, 2006St. FlorianLecture is canceled
Wed, May 10, 200610:15 - 11:45 Room: T 111Lecture 18
Thu, May 11, 200610:15 - 11:45 Room: T 111Lecture 19
Wed, May 17, 200610:15 - 11:45 Room: T 111Lecture 20
Thu, May 18, 200610:15 - 11:45 Room: T 111Lecture 21
Wed, May 24, 200610:15 - 11:45 Room: T 111Lecture 22
Thu, May 25, 2006Christi HimmelfahrtLecture is canceled
Wed, May 31, 200610:15 - 11:45 Room: T 111Lecture 23
Thu, June 1, 200610:15 - 11:45 Room: T 111Lecture 24
Wed, June 7, 200610:15 - 11:45 Room: T 111Lecture 25
Thu, June 8, 200610:15 - 11:45 Room: T 111Lecture 26
Wed, June 14, 200610:15 - 11:45 Room: T 111Lecture 27
Thu, June 15, 2006FronleichnamLecture is canceled
Wed, June 21, 200610:15 - 11:45 Room: T 111Lecture 28
Thu, June 22, 200610:15 - 11:45 Room: T 111Lecture 29
Wed, June 28, 200610:15 - 11:45 Room: T 111Lecture 30
Thu, June 29, 200610:15 - 11:45 Room: T 111Presentation
Information about the examination

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



Tutorial      up

Numerical Methods for Elliptic Partial Differential Equations - Tutorials

(CourseId 327.004, 2 hours per week, Semester 6)

Tutorials held by: Dr. Jan Valdman

Time and room:

Wed, March 15, 200610:15 - 11:45 Room: T 111Tutorial 01
Tue, March 21, 200610:15 - 11:45 Room: T 1010Tutorial 02
Tue, March 28, 200610:15 - 11:45 Room: T 1010Tutorial 03
Tue, April 4, 200610:15 - 11:45 Room: T 1010Tutorial 04
Tue, April 25, 200610:15 - 11:45 Room: T 1010Tutorial 05
Tue, May 9, 200610:15 - 11:45 Room: T 1010Tutorial 06
Tue, May 16, 200610:15 - 11:45 Room: T 1010Tutorial 07
Tue, May 23, 200610:15 - 11:45 Room: T 1010Tutorial 08
Tue, May 30, 200610:15 - 11:45 Room: T 1010Tutorial 09
Tue, June 6, 2006Pfingstdienstagcanceled
Tue, June 13, 200610:15 - 11:45 Room: T 1010Tutorial 10
Tue, June 20, 200610:15 - 11:45 Room: T 1010Tutorial 11
Tue, June 27, 200610:15 - 11:45 Room: T 1010Tutorial 12
Thu, June 29, 200610:15 - 11:45 Room: T 111Presentation of PA01-PA04

Exercises      up
Exercise 1March 15, 2006pdf
Exercise 2March 21, 2006pdf
Exercise 3March 28, 2006pdf
Exercise 4April 4, 2006pdf
Exercise 5April 25, 2006pdf
Exercise 6May 9, 2006pdf
Exercise 7May 16, 2006pdf
Exercise 8May 23, 2006pdf
Exercise 9May 30, 2006pdf
Exercise 10June 13, 2006pdf
Exercise 11June 20, 2006pdf
Exercise 12June 27, 2006pdf

Practical exercises      up
PA 01MAGNETpdf
PA 02CHAMBERpdf
PA 03BEAMpdf
PA 04TIMOSHENKO BEAMpdf

Transparencies      up
Transparency 05a: b/w1.3.1. Mixed VF I: General
Transparency 05b: b/w1.3.1. Mixed VF II: Navier-Stokes
Transparency 05c: b/w1.3.1. Mixed VF III: Oseen/Stokes
Transparency 05d: b/w1.3.1. Mixed VF IV: Poisson equ.
Transparency 05e: b/w1.3.1. Mixed VF V: 1st bih. BVP
Transparency 05f: b/w1.3.2. Dual VF I: General
Transparency 05g: b/w1.3.2. Dual VF II: Cont.
Transparency 05h: b/w1.3.2. Dual VF III: Example
Transparency 06a: b/wCourant's idea
Transparency 06b: colourIllustration
Transparency 07: colourRemark 2.1.1-2
Transparency 08: b/wRemark 2.1.3-4
Transparency 09: colourMesh for CHIP
Transparency 10: b/wCHIP.NET
Transparency 11: b/wMesh Generation 1.-2.
Transparency 12a: b/wMesh Generation 3.
Transparency 12b: colourMesh Generation 4.
Transparency 13a: colourstiffness matrix (1)
Transparency 13b: b/wstiffness matrix (2)
Transparency 13c: b/wstiffness matrix (3)
Transparency 14a: b/w2nd kind BC
Transparency 14b: b/w3rd kind BC
Transparency 14c: b/w1st kind BC
Transparency 15: colourIllustration
Transparency 16: b/wExercises 2.5 - 2.8
Transparency 17a: colourRoad Map I
Transparency 17b: b/wRoad Map II
Transparency 17c: colourTheorem 2.6
Transparency 18a: colourRemark 2.7.1
Transparency 18b: b/wRemark 2.7.2-5, E 2.9, E 2.10
Transparency 19: b/wTheorem 2.8 (H1-Convergence)
Transparency 20: b/wRemark 2.9.1-4
Transparency 21: b/wRemark 2.9.5
Transparency 22: b/wRemark 2.14
Transparency 23: colourVar.Crimes I
Transparency 24: colourVar.Crimes II
Transparency 25: colourVar.Crimes III
Transparency 26: b/wRemark 2.20
Transparency 27a: b/wDWR I
Transparency 27b: b/wDWR II
Transparency 27c: colourAFEM
Transparency 28: colourRemark 3.1
Transparency 29: colourExample, Remark 3.2
Transparency 30: b/wSecondary Grids I
Transparency 31: b/wSecondary Grids II
Transparency 32: colourRemark 3.3 + E 3.1
Transparency 33: b/wRemark 3.4
Transparency 34: colourBoundary boxes
Transparency 35: colourRemark 3.5 + E 3.2
Transparency 36a: b/wGalerkin-Petrov I
Transparency 36b: b/wGalerkin-Petrov II
Transparency 37a: b/wRemark 3.6.1-3.6.4
Transparency 37b: b/wRemark 3.6.5-3.6.6
Transparency 38: colourRef + Remark 3.7
Transparency 39: colourDiscrete Convergence I
Transparency 40: b/wDiscrete Convergence II
Transparency 41: b/wDiscrete Convergence III
Transparency 42: b/wDiscrete Convergence IV (E 3.3)
Transparency 43: b/wDiscrete Convergence V
Transparency 44: colourDiscrete Convergence VI
Transparency 39-44: b/wSummary
Transparency 45: b/w4. BEM 4.1 Introduction I
Transparency 46: b/w4.1 Introduction II
Transparency 47: b/w4.1 Introduction III
Transparency 48: b/w4.1 Introduction IV
Transparency 49a: b/wSubsection 4.2.1
Transparency 50a: colourSection 4.3: CM I
Transparency 50b: b/wSection 4.3: CM II
Transparency 51a: colourSection 4.3: CM III
Transparency 51b: b/wSection 4.3: CM IV
Transparency 52a: b/wSection 4.3: CM V
Transparency 52b: colourSection 4.3: CM VI
Transparency 53: b/wSection 4.3: CM VII
Transparency 54: b/wSection 4.3: CM VIII
Transparency 55: b/wSection 4.3: CM IV
Transparency 56: b/wSection 4.3: CM X
Transparency 57: b/wSection 4.3: CM XI
Transparency 58a: b/wBIO: Def.
Transparency 58b: b/wBIO: Calderon
Transparency 58c: b/wBIO: D2N
Transparency 59a: b/w4.4.2 Properties I
Transparency 59b: b/w4.4.2 Properties II
Transparency 60: b/wGalerkin I
Transparency 61: b/wGalerkin II
Transparency 62: b/wGalerkin III
Transparency 63: b/wGalerkin IV
Transparency 64: b/wGalerkin V

Basic Lecture Notes:      up
[1]   Langer U.: Numerik I (Operatorgleichungen), JKU, Linz 1996 (Sobolev-Spaces and Tools).
Postscript-File
[2]   Langer U.: Numerik II (Numerische Verfahren für Randwertaufgaben), JKU, Linz 1996 (FEM and FVM).
Postscript-File
[3]   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
[4]   Steinbach O.: Numerische Näherungsverfahren für elliptische Randwertprobleme. Teubner-Verlag, Stuttgart, Leipzig, Wiesbaden 2003 (FEM and BEM).
FEBEBook
[5]   Steinbach O.: Lösungsverfahren für lineare Gleichungssysteme: Algorithmen und Anwendungen. Teubner-Verlag, Stuttgart, Leipzig, Wiesbaden 2005 (solvers for systems of algebraic equations).

Additional Literature:      up
[1]   Braess D.: Finite Elemente. Springer Lehrbuch, Berlin, Heidelberg 1997.
[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.


Software:      up
FEM1D FEM2D NETREFINER FEM EP Mesh Generation


Links:      up

      NETGEN
      NGSolve
      SPIDER

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

Contents:
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.