Numerical Methods in Continuum Mechanics 1 | last update: 2021-09-30 |
[ Lecture ] [ Tutorial ] [ Exercises ] [ Transparencies ] [ Lecture Notes ] [ Additional Literature ] [ Software ] [ Links ] [ General ] [ Home ]
Lecture up
(CourseId 327.005, 2 hours per week, Semester 6)
Lecturer: O.Univ.-Prof. Dr. Ulrich Langer
Time and room:
Wed, Mar 2, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 1: Introduction |
Thu, Mar 3, 2016 | 10:15 - 11:45 Room: K 001A | Lecture 2 |
Wed, Mar 9, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 3 |
Thu, Mar 10, 2016 | 10:15 - 11:00 Room: K 001A | Lecture 4 |
Wed, Mar 16, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 5 |
Easter Break | ||
Wed, Apr 6, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 6 |
Wed, Apr 13, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 7 |
Wed, Apr 20, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 8 |
Wed, Apr 27, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 9 |
Wed, May 4, 2016 | Landespatron (no lecture) | |
Wed, May 11, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 10 |
Wed, May 18, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 11 |
Wed, May 25, 2016 | Canceled | |
Wed, Jun 1, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 12 |
Wed, Jun 8, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 13 |
Wed, Jun 15, 2016 | Canceled | |
Wed, Jun 22, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 14 |
Wed, Jun 29, 2016 | 10:15 - 11:45 Room: K 009D | Lecture 15 |
Prüfungsfragen: | up |
Prüfungstermine: | up |
Tutorial up
(CourseId 327.006, 1 hour per week, Semester 6)
Tutorials held by: O.Univ.-Prof. Dr. Ulrich Langer
Time and room:
Thu, Mar 17, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 01 |
Easter Break | ||
Thu, Apr 7, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 02 |
Thu, Apr 14, 2016 | Canceled | |
Thu, Apr 21, 2016 | 10:15 - 11:45 Room: K 001A | Tutorial 03-04 |
Thu, Apr 28, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 05 |
Thu, May 5, 2016 | Holiday | |
Thu, May 12, 2016 | 10:15 - 11:45 Room: K 001A | Tutorial 06-07 |
Thu, May 19, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 08 |
Thu, May 26, 2016 | Holiday | |
Thu, Jun 2, 2016 | Canceled | |
Thu, Jun 9, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 09 |
Thu, Jun 16, 2016 | Canceled | |
Thu, Jun 23, 2016 | 10:15 - 11:45 Room: K 001A | Tutorial 10-11 |
Thu, Jun 30, 2016 | 10:15 - 11:00 Room: K 001A | Tutorial 12 |
Exercises up
Tutorial 01 | Mar 17, 2016 | Trace Spaces | |
Tutorial 02 | Apr 7, 2016 | ||
Tutorial 03-04 | Apr 21, 2016 | ||
Tutorial 05 | Apr 28, 2016 | ||
Tutorial 06-07 | May 12, 2016 | ||
Tutorial 08 | May 19, 2016 | ||
Tutorial 09 | Jun 9, 2016 | ||
Tutorial 10 | Jun 23, 2016 | ||
Tutorial 11-12 | Jun 30, 2016 |
Transparencies up
Transparency 1: b/w | 1.1.1 Primal VF I |
Transparency 2: b/w | 1.1.1 Primal VF II |
Transparency 2a: colour | Example 1.3: I |
Transparency 2b: colour | Example 1.3: II |
Transparency 2c: colour | Theorem 1.4 |
Transparency 3: b/w | Corollaries 1.6/1.7 |
Transparency 4: b/w | 1.2.1 Nonlin. VP |
Transparency 5: colour | 1.2.2 VI 1 |
Transparency 6: colour | 1.2.2 VI 2 |
Transparency 7: colour | 1.2.2 VI 3 |
Transparency 7a: colour | Proof: Existence |
Transparency 7b: colour | Proof: Uniqueness+Nonexp. |
Transparency 8: b/w | Remark 2.1 |
Transparency 8a: colour | Exercises 2.3 and 2.5 |
Transparency 8b: colour | Lemma 2.8 |
Transparency 8c: colour | Proof |
Transparency 8d: colour | Theorem 2.9 |
Transparency 9: colour | 2.2 Sym. Case I |
Transparency 10: colour | 2.2 Sym. Case II |
Transparency 11: colour | 2.2 Sym. Case III |
Transparency 12: b/w | 2.2 Sym. Case IV |
Transparency 13: b/w | 2.2 Sym. Case V |
Transparency 14: colour | 2.2 Sym. Case VI |
Transparency 15: colour | 2.3 MVP(+) I |
Transparency 16: b/w | 2.3 MVP(+) II |
Transparency 17: b/w | 2.3 MVP(+) III |
Transparency 18: colour | 2.3 MVP(+) IV |
Transparency 19: colour | 2.4 Exercises |
Transparency 20: colour | 2.4.2 Arrow-Hurwicz |
Transparency 21: b/w | 2.4.3 Theorem 2.21 |
Transparency 22: b/w | 2.4.3 Proof I |
Transparency 23: colour | 2.4.3 Proof II |
Transparency 24: colour | 2.4.3 Proof III |
Transparency 25: colour | 2.4.3 Example 2.22 |
Transparency 26: colour | 2.4.3 Preconditioner |
Transparency 27: colour | 2.4.3 Excerises 2.24/25 |
Transparency 28: colour | 3.1. Basic equations |
Transparency 29: colour | 3.2.1 Derivation PVF |
Transparency 30: colour | 3.2.1 PVF=MP |
Transparency 31: colour | 3.2.1 Ass. L&M |
Transparency 32: b/w | 3.2.1 RBM |
Transparency 33: b/w | 3.2.1 1st KORN |
Transparency 34: b/w | 3.2.1 KORN's ineq. |
Transparency 35: b/w | 3.2.1 2nd KORN |
Transparency 36: b/w | 3.2.1 L&M |
Transparency 37: b/w | 3.2.1 Exercise 3.8 |
Transparency 38: colour | 3.2.1 FEM |
Transparency 39: colour | 3.2.2 HRP I 1 |
Transparency 40: b/w | 3.2.2 HRP I 2 |
Transparency 41: b/w | 3.2.2 HRP I 3 |
Transparency 42: colour | 3.2.2 HRP I 4 |
Transparency 43: colour | 3.2.2 HRP II MFEM |
Transparency 44a: b/w | Punkt 3.2.3. I |
Transparency 44b: b/w | Punkt 3.2.3. II |
Transparency 44c: b/w | Punkt 3.2.3. III |
Transparency 44d: b/w | Punkt 3.2.3. IV |
Transparency 44e: b/w | Punkt 3.2.3. V |
Transparency 45: colour | FE-Discr. |
Transparency 46: colour | FE-System |
Basic Lecture Notes up
- Langer U.: Numerische Festkörpermechanik (Computational Mechanics), JKU, Linz 1997. PS-File
- Zulehner W.: Lecture Notes for the Course Numerical Methods for Continuum Mechanics 1, JKU, Linz 2006. pdf-File
Additional Literature up
- Braess D.: Finite Elemente: Theorie, schnelle Löser und Anwendungen in der Elastizitätstheorie. Springer Lehrbuch, Berlin, Heidelberg 1997, see also Braess' homepage
- Braess D.: Finite Elements: Theory, Fast Solvers and Applications in Solid Mechanics. Cambridge University Press, Cambridge, 1997, 2001, 2007. (= english version of [1])
- Brezzi F., Fortin M.: Mixed and Hybrid Finite Element Methods. Springer Series in Computational Mathematics, Vol. 15, Springer-Verlag, New York 1991.
Software up
Links up
General Information up
Previous Knowledge:
- 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
- Modelling
- Numerical Methods for Partial Differential Equations
- Special Topics in Computational Mathematics
- Special Seminars in Computational Mathematics
Get knowledge of analysis tools and of numerical methods for mechanical problems
Contents:- Introduction
- Analysis and numerics of mixed boundary value problems
- Modelling, analysis and numerics of linear elasticity problems
- Structural mechanics
- The tutorial to this lecture treats numerical methods for the solution of mechanical problems and has 1 hour per week
- First Tutorial: Thursday, March 17, 2016, 10:15 - 11:00, Room K 001A
Lecture: oral
Tutorial:
The mark of the tutorial consists of the
assessment of the individual exercises and the presentations on the blackboard.