Seminar on Numerical Analysis

letzte Änderung: 2021-09-30
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Seminar on Numerical Analysis

Discontinuous Petrov-Galerkin (DPG) Methods

(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, 2017-10-10, 13:45 - 15:15 Uhr, Room: S2 054

Time, room, seminar, student, supervisor:

Tue, 2017-10-1013:45 - 15:15 Room: S2 054IntroductionZulehner
Tue, 2017-10-1713:45 - 15:15 Room: S2 054Seminar 01JodlbauerZulehner
Tue, 2017-10-2413:45 - 15:15 Room: S2 054Hackbusch's lecture
Tue, 2017-10-3113:45 - 15:15 Room: S2 054Hackbusch's lecture
Tue, 2017-11-0713:45 - 15:15 Room: S2 054Seminar 02Mandlmayr, SchwalsbergerLanger
Tue, 2017-11-1413:45 - 15:15 Room: S2 054Seminar 03SchafelnerGfrerer
Tue, 2017-11-2113:45 - 15:15 Room: S2 054Seminar 04MitterZulehner
Tue, 2017-11-2813:45 - 15:15 Room: S2 054Seminar 05EndtmayerLanger
Tue, 2017-12-0513:45 - 15:15 Room: S2 054Seminar 06SchwalsbergerZulehner
Tue, 2017-12-1213:45 - 15:15 Room: S2 054Seminar 07MandlmayrLanger
Tue, 2017-12-1215:30 - 15:15 Room: S2 416-1Gopalakrishnan's talk
Tue, 2018-01-0913:45 - 15:15 Room: S2 054Seminar 08EndtmayerLanger
Tue, 2018-01-1613:45 - 15:15 Room: S2 054Seminar 09SchafelnerLanger
Tue, 2018-01-2313:45 - 15:15 Room: S2 054Seminar 10JodlbauerZulehner
Tue, 2018-01-3013:45 - 15:15 Room: S2 054Seminar 11MitterZulehner
Tue, 2018-01-3015:30 - 15:15 Room: S2 416-1Seminar 12SchneckenleitnerLanger


- Seminar Topics up

Introduction:2017-10-10
Introduction by Zulehner
Seminar 01:2017-10-17
Title: A class of discontinuous Petrov-Galerkin (DPG) methods: otpimal test functions
Literature:   small parts from [1], [2], [3], [4], [5], [6], [7]
Supervisor: Zulehner
Student:     Jodlbauer
Seminar 02:2017-11-07
Title: DPG methods for pure convection in 1D and 2D
Literature:   [1] and [2]
Supervisor: Langer
Students:     Mandlmayr, Schwalsberger
Seminar 03:2017-11-14
Title: DPG methods for convection dominated diffusion in 1D and 2D
Literature:   [2]
Supervisor: Gfrerer
Student:     Schafelner
Seminar 04:2017-11-21
Title: DPG methods for time-harmonic wave propagation in 1D
Literature:    [4]
Supervisor: Zulehner
Student:     Mitter
Seminar 05:2017-11-28
Title: Adaptivity
Literature:    [3]
Supervisor: Langer
Student:     Endtmayer
Seminar 06:2017-12-05
Title: Analysis of the DPG method for the Poisson equation
Literature:    [8]
Supervisor: Zulehner
Student:     Schwalsberger
Seminar 07:2017-12-12
Title: An analysis of the practical DPG method
Literature:    [9]
Supervisor: Langer
Student:     Mandlmayr
Seminar 08:2018-01-09
Title: A posteriori error control for DPG methods
Literature:    [5]
Supervisor: Langer
Student:     Endtmayer
Seminar 09:2018-01-16
Title: Robust DPG method for convection-dominated diffusion problem
Literature:    [11]
Supervisor: Langer
Student:     Schafelner
Seminar 10:2018-01-23
Title: The DPG method for the Stokes problem
Literature:    [12]
Supervisor: Zulehner
Student:     Jodlbauer
Seminar 11:2018-01-30
Title: DPG method with optimal test functions for thin-body problems in solid mechanics
Literature:    [10]
Supervisor: Zulehner
Student:     Mitter
Seminar 12:2018-01-30
Title: Space-time DPG methods
Literature:    [13]
Supervisor: Langer
Student:     Schneckenleitner


- Literature up

[1]   L. Demkowicz and J. Gopalakrishnan. A class of discontinuous Petrov-Galerkin methods. I: The transport equation. Comput. Methods Appl. Mech. Eng., 199(23-24):1558-1572, 2010.
[2]   L. Demkowicz and J. Gopalakrishnan. A class of discontinuous Petrov-Galerkin methods. II: Optimal test functions. Numer. Methods Partial Differ. Equations, 27(1):70- 105, 2011.
[3]   Leszek Demkowicz, Jay Gopalakrishnan, and Antti H. Niemi. A class of discontinuous Petrov-Galerkin methods. III: Adaptivity. Appl. Numer. Math., 62(4):396-427, 2012.
[4]   J. Zitelli, I. Muga, L. Demkowicz, J. Gopalakrishnan, D. Pardo, and V.M. Calo. A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time- harmonic wave propagation in 1D. J. Comput. Phys., 230(7):2406-2432, 2011.
[5]   Carsten Carstensen, Leszek Demkowicz, and Jay Gopalakrishnan. A posteriori error control for DPG methods. SIAM J. Numer. Anal., 52(3):1335-1353, 2014.
[6]   J. Gopalakrishnan. Five lectures on DPG methods. ArXiv e-prints, June 2013.
[7]   Jay Gopalakrishnan. Theoretical & practical aspects of dpg methods. Plenary Talk at the 11th International Conference on Large-Scale Scientific Computations, June 5 - 9, 2017, Sozopol, Bulgaria.
[8]   L. Demkowicz and J. Gopalakrishnan. Analysis of the DPG method for the Poisson equation. SIAM J. Numer. Anal., 49(5):1788-1809, 2011.
[9]   J. Gopalakrishnan and W. Qiu. An analysis of the practical DPG method. Math. Comput., 83(286):537-552, 2014.
[10]   Antti H. Niemi, Jamie A. Bramwell, and Leszek F. Demkowicz. Discontinuous Petrov- Galerkin method with optimal test functions for thin-body problems in solid mechanics. Comput. Methods Appl. Mech. Eng., 200(9-12):1291-1300, 2011.
[11]   Leszek Demkowicz and Norbert Heuer. Robust DPG method for convection-dominated diffusion problems. SIAM J. Numer. Anal., 51(5):2514-2537, 2013.
[12]   Nathan V. Roberts, Tan Bui-Thanh, and Leszek Demkowicz. The DPG method for the Stokes problem. Comput. Math. Appl., 67(4):966-995, 2014.
[13]   J. Gopalakrishnan and P. Sepulveda. A spacetime DPG method for acoustic waves, arXiv:1709.08268 [math.NA], September 2017.
[14]   L. Demkowicz, J. Gopalakrishnan, S. Nagaraj, and P. Sepúlveda. A spacetime DPG method for the Schrödinger equation. SIAM Journal on Numerical Analysis, 55(4):1740 - 1759, 2017.

- Participants up

Endtmayer Bernhard
Jodlbauer Daniel
Mandlmayr Michael
Mitter Ludwig
Schafelner Andreas
Schneckenleitner Rainer
Schwalsberger Martin

- General Remarks up