Institute of Numerical Mathematics - Seminar Numerical Analysis

Seminar Numerical Analysis: Adaptive Finite Element Methods

Date	Speaker	Supervisor	Title	Literature
2019-10-08	U. Langer		Introduction
2019-10-22	B. Endtmayer	H. Gfrerer	Convergence of AFEM	[1]
2019-11-05	L. Mitter	W. Zulehner	Data oscillation and convergence of adaptive FEM	[2]
2019-11-26	M. Gobrial	W. Zulehner	Newest vertex bisection method	[3]
2019-12-10	D. Jodlbauer	W. Zulehner	Optimality of a standard AFEM	[4]
2020-01-07	R. Schneckenleitner	U. Langer	Axioms of Adaptivity I	[5], Sections 1 - 3, i.e. pp. 1195 - 1207,Subsection 5.1
2020-01-21	A. Schafelner	U. Langer	Axioms of Adaptivity II	[5], Sections 4 + Subsection 5.1, i.e. pp. 1207 -1217

Date

Speaker

Supervisor

Title

Literature

2019-10-08

U. Langer

Introduction

2019-10-22

B. Endtmayer

H. Gfrerer

Convergence of AFEM

[1]

2019-11-05

L. Mitter

W. Zulehner

Data oscillation and convergence of adaptive FEM

[2]

2019-11-26

M. Gobrial

W. Zulehner

Newest vertex bisection method

[3]

2019-12-10

D. Jodlbauer

W. Zulehner

Optimality of a standard AFEM

[4]

2020-01-07

R. Schneckenleitner

U. Langer

Axioms of Adaptivity I

[5], Sections 1 - 3, i.e. pp. 1195 - 1207,Subsection 5.1

2020-01-21

A. Schafelner

U. Langer

Axioms of Adaptivity II

[5], Sections 4 + Subsection 5.1, i.e. pp. 1207 -1217

Literature

[1] W. Dörfler, Convergent Adaptive Algorithm for Poisson's Equation. SIAM J. Numer. Anal., 33(3), p. 1106-1124, 1996.

[2] P. Morin, R. Nochetto, and K. Siebert. Data oscillation andconvergence of adaptive FEM. SIAM J. Numer. Anal., 38(2), p. 466-488, 2000.

[3] P. Binev, W. Dahmen, and R. DeVore. Adaptive finite elementmethods withconvergence rates. Numer. Math., 97(2), p. 219-268, 2004.

[4] R. Stevenson, Optimality of a standard adaptive finiteelement method, Found. Comput. Math. 7 (2), p. 245-269, 2007.

[5] C. Carstensen, M. Feischl, M. Page, and C. Praetorius. Axiomsof adaptivity. Comput. Methods Appl. Math. 67, p. 1195-1253, 2014.

Additional Literature

[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.

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