Seminar on Numerical Analysis |
letzte Änderung: 2021-09-30 |
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Seminar on Numerical Analysis
Adaptive Finite Element Methods (AFEM)
(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, 2019-10-08, 13:45 - 15:15 Uhr, Room: S2 054
Time, room, seminar, student, supervisor:
Tue, 2019-10-08 | 13:45 - 15:15 Room: S2 054 | Seminar 01: Introduction | Langer | |
Tue, 2019-10-15 | 13:45 - 15:15 Room: S2 054 | Consultation | ||
Tue, 2019-10-22 | 13:45 - 15:15 Room: S2 054 | Seminar 02 | Endtmayer | Gfrerer |
Tue, 2019-10-29 | 13:45 - 15:15 Room: S2 054 | Consultation/WS2 RICAM | ||
Tue, 2019-11-05 | 13:45 - 15:15 Room: S2 054 | Seminar 03 | Mitter | Zulehner |
Tue, 2019-11-12 | 13:45 - 15:15 Room: S2 054 | Consultation | ||
Tue, 2019-11-19 | 13:45 - 15:15 Room: S2 054 | Consultation | ||
Tue, 2019-11-26 | 13:45 - 15:15 Room: S2 054 | Seminar 04 | Gobrial | Zulehner |
Tue, 2019-12-03 | 13:45 - 15:15 Room: S2 054 | cont. | ||
Tue, 2019-12-10 | 13:45 - 15:15 Room: S2 054 | Seminar 05 | Jodlbauer | Zulehner |
Tue, 2019-12-17 | 13:45 - 15:15 Room: S2 054 | cont. | ||
Tue, 2020-01-07 | 13:45 - 15:15 Room: S2 054 | Seminar 06 | Schneckenleitner | Langer |
Tue, 2020-01-14 | 13:45 - 15:15 Room: S2 054 | cont. | ||
Tue, 2020-01-21 | 13:45 - 15:15 Room: S2 054 | Seminar 07 | Schafelner | Langer |
Tue, 2020-01-28 | 13:45 - 15:15 Room: S2 054 | cont. |
Seminar Topics | up |
The seminar deals with the theoretical aspects of AFEM for elliptic BVP such as
> Reliability of a posteriori error estimates
> Efficiency of a posteriori error estimates
> Constants
> Computable bounds
> Convergence
> Convergence rates
but also with a posteriori error estimates and AFEM for
> parabolic initial-boundary value problems
> hyperbolic problems
> optimal control problems
Seminar 01: | 2019-10-08 Introduction by Langer |
Seminar 02: | 2019-10-22 Title: Convergence of AFEM Literature: [1] Supervisor: Gfrerer Student: Endtmayer |
Seminar 03: | 2019-11-05 Title: Data oscillation and convergence of adaptive FEM Literature: [2] Supervisor: Zulehner Student: Mitter |
Seminar 04: | 2019-11-26 Title: Newest vertex bisection method Literature: [3] Supervisor: Zulehner Student: Gobrial |
Seminar 05: | 2019-12-10 Title: Optimality of a standard AFEM Literature: [4] Supervisor: Zulehner Student: Jodlbauer |
Seminar 06: | 2020-01-07 Title: Axioms of Adaptivity I Literature: [5], Sections 1 - 3, i.e. pp. 1195 - 1207,Subsection 5.1 Supervisor: Langer Student: Schneckenleitner |
Seminar 07: | 2020-01-21 Title: Axioms of Adaptivity II Literature: [5], Sections 4 + Subsection 5.1, i.e. pp. 1207 -1217 Supervisor: Langer Student: Schafelner |
Literature | up |
[1] W. Dörfler, Convergent Adaptive Algorithm for Poisson’s Equation. SIAM J. Numer. Anal., 33(3), 1106–1124.
[2] P. Morin, R. Nochetto, and K. Siebert. Data oscillation andconvergence of adaptive FEM. SIAM J. Numer. Anal., 38(2):466–488,2000.
[3] P. Binev, W. Dahmen, and R. DeVore. Adaptive finite elementmethods withconvergence rates. Numer. Math., 97(2):219 – 268, 2004.
[4] R. Stevenson, Optimality of a standard adaptive finiteelement method, Found. Comput. Math. 7 (2) (2007) 245–269.
[5] C. Carstensen, M. Feischl, M. Page, and C. Praetorius. Axiomsof adaptivity. Comput. Methods Appl. Math. 2014; 67:1195-1253.
Additional Literature: Books on AFEM | up |
[A] R. Verfürth, A Review of A Posteriori Error Estimation and Adaptive Mesh-Refinement Techniques. Wiley-Teubner, 1996 (150 pp).
[B] R. Verfürth, A Posteriori Error Estimation Techniques for Finite Element Methods. Oxford University Press, 2013 (416 pp).
[C] M. Ainsworth, J.T. Oden, A posteriori error estimation infinite element analysis, in: Pure and Applied Mathematics (New York),Wiley-Interscience, New York, 2000.
[D] I. Babuska, T. Strouboulis, The finite element method andits reliability, in: Numerical Mathematics and Scientific Computation, Oxford University Press, New York, 2001.
[E] P. Neittaanmäki, S. Repin, Reliable Methods for Computer Simulation, in: Studies in Mathematics and its Applications, vol. 33,Elsevier Science B.V, Amsterdam, 2004.
[F] S. Repin, A Posteriori Estimates for Partial Differential Equations, in: Radon Series on Computational and Applied Mathematics,vol. 4, Walter de Gruyter GmbH & Co. KG, Berlin, 2008.
[G] W. Han, A POSTERIORI ERROR ANALYSIS VIA DUALITY THEORY. With Applications in Modeling and Numerical Approximations. Springer, New York, 2005.
Participants | up |
Endtmayer Bernhard
Gobrial Mario
Jodlbauer Daniel
Mitter Ludwig
Pistrich Mario
Schafelner Andreas
Schneckenleitner Rainer
General Remarks | up |