Seminar on Numerical Analysis

letzte Änderung: 2021-10-01

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Seminar on Numerical Analysis

Interpolation Spaces and Applications in Numerical Analysis

(Course Id 327.050, 2 hours per week, semester 5)

Supervisors: A.Univ.-Prof. Dr. Helmut Gfrerer

                       O.Univ.-Prof. Dr. Ulrich Langer

                       A.Univ.-Prof. Dr. Walter Zulehner

Start of the seminar: Tue, 2010-10-05, 13:45 - 15:15 Uhr, Room: T 211

Time, room, seminar, student, supervisor:

Tu, 2010-10-0513:45 - 15:15 Room: T 211Introduction
Tu, 2010-10-1213:45 - 15:15 Room: T 211Consultation
Tu, 2010-10-1913:45 - 15:15 Room: T 211Seminar 01
Tu, 2010-10-26National holiday
Tu, 2010-11-02Holiday
Tu, 2010-11-0913:45 - 15:15 Room: T 211Seminar 02
Tu, 2010-11-1613:45 - 15:15 Room: T 211Seminar 03
Tu, 2010-11-2313:45 - 15:15 Raum: T 211Seminar 04
Tu, 2010-11-3013:45 - 15:15 Raum: T 211Seminar 05
Tu, 2010-12-0713:45 - 15:15 Raum: T 211Seminar 06
Tu, 2010-12-1413:45 - 15:15 Raum: T 211Seminar 07
Tu, 2011-01-1113:45 - 15:15 Raum: T 211Seminar 08
Tu, 2011-01-1813:45 - 15:15 Raum: T 211Seminar 9
Tu, 2011-01-2513:45 - 15:15 Raum: T 211Seminar 10


- Seminar Topics up

Introduction:2010-10-05
Introduction by Walter Zulehner
Seminar 01:2010-10-19
Title: Interpolation in R^n
Literature:   [1]
Supervisor: W. Zulehner
Student:     Leyew, Zeleke
Seminar 02:2010-11-09
Title: K-Method: Interpolation Spaces and the interpolation theorem
Literature:    [4] pp. 208 - 221
Supervisor: W. Zulehner
Student:     Mutimbu, Vlcek
Seminar 03:2010-11-16
Title: J-Method
Literature:    [4] pp. 208 - 221
Supervisor: U. Langer
Student:     Kowalska
Seminar 04:2010-11-23
Title: The reiteration theorem and the duality theorem
Literature:    [4] pp. 208 - 221 and [2]
Supervisor: W. Zulehner
Student:     Kollmann
Seminar 05:2010-11-30
Title: Alternative approaches
Literature:    [5]
Supervisor: H. Gfrerer
Student:     Kolmbauer
Seminar 06:2010-12-07
Title: Finite Element Convergence Estimates
Literature:    [3], pp. 282 - 284
Supervisor: W. Zulehner
Student:     Leyew, Zeleke
Seminar 07:2010-12-14
Title: Real Interpolation of Sobolev Spaces
Literature:    [3], pp. 279 - 281, [7], pp. 79 - 80, 329 - 330, [9]
Supervisor: U. Langer
Student:     Mutimbu, Vlcek
Seminar 08:2011-01-11
Title: Preconditioners for Saddle Point Problems by Interpolation
Literature:    [6]
Supervisor: W. Zulehner
Student:     Kollmann
Seminar 09:2011-01-18
Title: Multilevel Representations, Space Interpolation and Preconditioning I
Literature:    Bramble's lecture notes, [10]
Supervisor: U. Langer
Student:     Kowalska
Seminar 10:2011-01-25
Title: Multilevel Representations, Space Interpolation and Preconditioning II
Literature:    Bramble's lecture notes, [8], pp. 306 - 319, [10]
Supervisor: U. Langer
Student:     Kolmbauer


- Literature up

[1]   W.Zulehner. Interpolation in R^n
[2]   J.Bergh, J.Löfström. Interpolation Spaces, An Introduction. Springer, Berlin, Heidelberg, New York (1976)
[3]   S.C.Brenner, L.R.Scott. The Mathematical Theory of Finite Element Methods. Springer, New York (1994)
[4]   R.A.Adams, J.J.F.Fournier. Sobolev Spaces, Second Edition. Vol. 140 in Pure and Applied Mathematics series, Elsevier (2008)
[5]   J.L.Lions, E. Magenes. Non-homogeneous boundary value problems and applications, Vol 1. Springer, Berlin (1972)
[6]   W. Zulehner. Non-standard norms and robust estimates for saddle point problems. Numa-Report 2010-07, pdf
[7]   W. McLean. Strongly Elliptic Systems and Boundary Integral Equations. Cambridge University Press 2000
[8]   O. Steinbach. Numerical Approximation Methods for Elliptic Boundary Value Problems: Finite and Boundary Elements. Springer (2008).
[9]   L.D. Mutimbu, M. Vlcek. Real Interpolation of Sobolev Spaces. Seminar-Report, JKU, Linz 2010.
[10]   M. Kolmbauer, M. Kowalska. Multilevel Representations, Space Interpolation and Preconditioning. Seminar-Report, JKU, Linz 2010.
[11]   L. Tartar. An Introduction to Sobolev Spaces and Interpolation Spaces. Lecture Notes of the Unione Matematica Italiana (UMI). Springer, Berlin, Heidelberg (2007).

- Participants up

Kollmann Markus
Kolmbauer Michael
Kowalska Monika
Leyew Bahru
Mutimbu Lawrence Dzidzai
Vlcek Martin
Zeleke Abiy Dejenee

- General Remarks up