Seminar on Numerical Analysis

letzte Änderung: 2017-03-29

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Seminar on Numerical Analysis

Space-Time Methods for PDEs

(Course Id 327.014, 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, 2016-10-11, 13:45 - 15:15 Uhr, Room: S2 059

Time, room, seminar, student, supervisor:

Tue, 2016-10-1113:45 - 15:15 Room: S2 059IntroductionLanger
Tue, 2016-10-1813:45 - 15:15 Room: S2 059Consultations
Tue, 2016-10-2513:45 - 15:15 Room: S2 059Seminar 01EndtmayerGfrerer
Tue, 2016-11-01Holiday (Allerheiligen)
Tue, 2016-11-0813:45 - 15:15 Room: S2 059Workshop on Space-Time Methods
Tue, 2016-11-1513:45 - 15:15 Room: S2 059Seminar 02SchafelnerLanger
Tue, 2016-11-2213:45 - 15:15 Room: S2 059Seminar 03RafetsederZulehner
Tue, 2016-11-2913:45 - 15:15 Room: S2 059Seminar 04HoferZulehner
Tue, 2016-12-0613:45 - 15:15 Room: S2 059School on SPDEs
Tue, 2016-12-1313:45 - 15:15 Room: S2 059Seminar 05/06Endtmayer, Faghfouri, ScholzLanger
Tue, 2017-01-1013:45 - 15:15 Room: S2 059Seminar 07SchafelnerLanger
Tue, 2017-01-1713:45 - 15:15 Room: S2 059Seminar 08JodlbauerNeumüller
Tue, 2017-01-2413:45 - 15:15 Room: S2 059Seminar 09Faghfouri, ScholzLanger
Tue, 2017-01-3113:45 - 15:15 Room: S2 059Seminar 10Hofer, RafetsederZulehner


- Seminar Topics up

Introduction:2016-10-11
Introduction by U. Langer
Seminar 01:2016-10-25
Title: First Initial-Boundary Value Problem for the Heat Equation
Literature:   [1], pp. 108 - 115
Supervisor: H. Gfrerer
Student:     B. Endtmayer
Seminar 02:2016-11-15
Title: First Initial-Boundary Value Problem for General Parabolic Equations
Literature:   [1], pp. 115 - 121
Supervisor: U. Langer
Student:     A. Schafelner
Seminar 03:2016-11-22
Title: The First Initial-Boundary Value Problem for Hyperbolic Equations
Literature:   [1], pp. 156 - 161
Supervisor: W. Zulehner
Student:     K. Rafetseder
Seminar 04:2016-11-29
Title: Space-time finite element methods for elastodynamics: formulation and error estimates
Literature:    [2]
Supervisor: W. Zulehner
Student:     C. Hofer
Seminar 05/06:2016-12-13
Title: A Space-Time Petrov-Galerkin method for linear wave equations
Title: A Space-Time Petrov-Galerkin method for linear wave equations following
Title: A Space-Time Petrov-Galerkin method for linear wave equations - Talk No. 2
Literature:    [3]
Additional literature:    [4]
Supervisor: U. Langer
Students:     B. Endtmayer, S. Faghfouri, F. Scholz
Seminar 07:2017-01-10
Title: Space–time finite element methods for parabolic problems
Literature:    [5]
Supervisor: U. Langer
Student:     A. Schafelner
Seminar 08:2017-01-17
Title: dG space–time methods for parabolic problems
Literature:    [6], pp. 5 - 33
Supervisor: M. Neumüller
Student:     D. Jodlbauer
Seminar 09:2017-01-24
Title: Stability of Petrov-Galerkin discretizations: Application to the space-time weak formulation for parabolic evolution problems
Title: Stability of Petrov-Galerkin discretizations: Application to the space-time weak formulation for parabolic equations - Talk No. 2
Literature:    [7]
Supervisor: U. Langer
Students:     S. Faghfouri, F. Scholz
Seminar 10:2017-01-31
Title: Space–time adaptive wavelet methods for parabolic evolution problems
Title: An overview of discretizations for space time methods
Literature:    [8]
Supervisor: W. Zulehner
Students:     C. Hofer, K. Rafetseder


- Literature up
[1]   O. A. Ladyzhenskaya. The Boundary Value Problems of Mathematical Physics. Springer-Verlag New York, 1985.
[2]   T.J.R. Hughes, G.M. Hulbert. Space-time finite element methods for elastodynamics: formulation and error estimates. Computer Methods in Applied Mechanics and Engineering, 66 (1988) 339-363.
[3]   C. Wieners. A Space-Time Petrov-Galerkin method for linear wave equations. Summer School, Zurich 2016, available at http://www.math.kit.edu/user/~wieners/SpaceTimeWave.pdf
[4]   W. Dörfler, S. Findeisen, C. Wieners: Space-time discontinuous galerkin discretizations for linear first-order hyperbolic evolution systems. Comput. Methods Appl. Math., 16(3):409–428, 2016.
[5]   O. Steinbach: Space–time finite element methods for parabolic problems. Comput. Methods Appl. Math., 15, 551-566, 2015.

[6]   M. Neumüller. Space-Time Methods: Fast Solvers and Applications. Dissertation, Graz University of Technology, June 2013.
[7]   C. Mollet. Stability of Petrov-Galerkin discretizations: Application to the space-time weak formulation for parabolic evolution problems, CMAM, 2014.
[8]   C. Schwab, R. Stevenson: Space–time adaptive wavelet methods for parabolic evolution problems. Math. Comput., 78, 1293–1318, 2009.

- Participants up

Endtmayer Bernhard
Faghfouri Sahar
Gangl Peter
Hofer Christoph
Jodlbauer Daniel
Rafetseder Katharina
Schafelner Andreas
Scholz Felix

- General Remarks up