Seminar on Numerical Analysis

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

Virtual Element Methods (VEM)

(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, 2018-10-02, 13:45 - 15:15 Uhr, Room: S2 346

Time, room, seminar, student, supervisor:

Tue, 2018-10-0213:45 - 15:15 Room: S2 346Seminar 01: IntroductionLanger
Tue, 2018-10-0913:45 - 15:15 Room: S2 346Consultation
Tue, 2018-10-1613:45 - 15:15 Room: S2 346Seminar 02MitterLanger
Tue, 2018-10-2313:45 - 15:15 Room: S2 346Seminar 03EndtmayerLanger
Tue, 2018-10-3013:45 - 15:15 Room: S2 346Seminar 04SchafelnerLanger
Tue, 2018-11-0613:45 - 15:15 Room: S2 346Consultation
Tue, 2018-11-1313:45 - 15:15 Room: S2 346Seminar 05SchneckenleitnerLanger
Tue, 2018-11-2013:45 - 15:15 Room: S2 346Seminar 06JodlbauerZulehner
Tue, 2018-11-0613:45 - 15:15 Room: S2 346Consultation
Tue, 2018-12-0413:45 - 15:15 Room: S2 346Seminar 07JodlbauerZulehner
Tue, 2018-11-0613:45 - 15:15 Room: S2 346Consultation
Tue, 2019-01-0813:45 - 15:15 Room: S2 346Seminar 08SchneckenleitnerLanger
Tue, 2019-01-1513:45 - 15:15 Room: S2 346Seminar 09EndtmayerLanger
Tue, 2019-01-2213:45 - 15:15 Room: S2 346Seminar 10SchafelnerZulehner
Tue, 2019-01-2913:45 - 15:15 Room: S2 346Seminar 11MitterZulehner


- Seminar Topics up

Seminar 01:2018-10-02
Introduction by Langer
Seminar 02:2018-10-16
Title: Polygonal and polyhedral meshes
Literature:   [1], Section 2.3, pp. 16 - 30
Supervisor: U. Langer
Student:     L. Mitter
Seminar 03:2018-10-23
Title: Basis and interpolation operators (smooth functions)
Literature:   [1], Section 2.3 - 2.5, pp. 31 - 51
Supervisor: U. Langer
Student:     B. Endtmayer
Seminar 04:2018-10-30
Title: Interpolation of non-smooth functions
Literature:   [1], Section 3.1 - 3.3, pp. 59 - 70
Supervisor: U. Langer
Student:     A. Schafelner
Seminar 05:2018-11-13
Title: Anisotropic Case
Literature:   [1], Section 3.4, pp. 70 - 90
Supervisor: U. Langer
Student:     R. Schneckenleitner
Seminar 06:2018-11-20
Title: Basic Principles of Virtual Element Methods
Literature:   [2]
Supervisor: W. Zulehner
Student:     D. Jodlbauer
Seminar 07:2018-12-04
Title: Computable VE approximation
Literature:   [3]
Supervisor: W. Zulehner
Student:     D. Jodlbauer
Seminar 08:2019-01-08
Title: VEM for general 2nd-order elliptic BVP
Literature:   [4]
Supervisor: U. Langer
Student:     R. Schneckenleitner
Seminar 09:2019-01-15
Title: A posteriori error estimates for the VEM and AVEM
Literature:   [5]
Supervisor: U. Langer
Student:     B. Endtmayer
Seminar 10:2019-01-22
Title: Divergence free VEM for Stokes
Literature:   [6]
Supervisor: W. Zulehner
Student:     A. Schafelner
Seminar 11:2019-01-29
Title: VEM for plates
Literature:   [7] VEM for plates
Supervisor: W. Zulehner
Student:     L. Mitter


- Literature up

[1]   S. Weiίer, BEM-based Finite Element Approaches on Polytopal Meshes, Manuskript, 2018.
[2]   L. Beirao da Veiga, F. Brezzi, A. Cangiani, G. Manzini, L.D. Marini, A. Russo, Basicprinciples of virtual element methods. Math. Models Methods Appl. Sci. 23 (1), 199–214(2013).
[3]   L. Beirao da Veiga, F. Brezzi, L.D. Marini, A. Russo, The hitchhiker's guide to the virtual element method, Math. Models Methods Appl. Sci. 24, 1541–1573 (2014).
[4]   L. Beirao da Veiga, F. Brezzi, L. D. Marini and A. Russo, Virtual element methods forgeneral second order elliptic problems on polygonal meshes, Math. Models Methods Appl. Sci. 26 (2016) 729–750.
[5]   A. Cangiani, E. Georgoulis, T. Pryer, O. J. Sutton, A posteriori error estimates for the virtual element method,Numerische Mathematik, 137 (4), 857–893 (2017)
[6]   L. Beirao da Veiga, C. Lovadina and G. Vacca, Divergence free virtual elements forthe Stokes problem on polygonal meshes, ESAIM : Math. Models Numer. Anal. 51 (2017) 509–535.
[7]   F. Brezzi and L. D. Marini, Virtual element methods for plate bending problems,Comput. Methods Appl. Mech. Eng. 253 (2013) 455–462.

- Additional Literature up

[*]   Beirao da Veiga, L., Brezzi, F., Marini, L.: Virtual elements for linear elasticity problems.SIAM J. Numer. Anal. 51(2), 794–812 (2013)
[*]   L. Beirao da Veiga, C. Lovadina and A. Russo, Stability analysis for the virtualelement method, arXiv:1607.05988.
[*]   M. F. Benedetto, S. Berrone, A. Borio, S. Pieraccini and S. Scialo?, A hybrid mortarvirtual element method for discrete fracture network simulations, J. Comput. Phys.306 (2016) 148–166.
[*]   M. F. Benedetto, S. Berrone, S. Pieraccini and S. Scialo?, The virtual element methodfor discrete fracture network simulations, Comput. Methods Appl. Mech. Eng. 280(2014) 135–156.
[*]   F. Brezzi, R. S. Falk and L. D. Marini, Basic principles of mixed virtual elementmethods, ESAIM: Math. Model. Numer. Anal. 48 (2014) 1227–1240.
[*]   Beirao da Veiga, L., Chernov, A., Mascotto, L., Russo, A.: Exponential convergence of the hpvirtual element method in presence of corner singularities. Numer. Math. 138(3), 581–613 (2018)
[*]   Gain, A.L., Talischi, C., Paulino, G.H.: On the virtual element method for three-dimensionallinear elasticity problems on arbitrary polyhedral meshes. Comp. Methods Appl. Mech. Engrg. 282, 132–160 (2014)

- Participants up

Endtmayer Bernhard
Jodlbauer Daniel
Mitter Ludwig
Schafelner Andreas
Schneckenleitner Rainer

- General Remarks up