Dr. Stefan Kinzel

Philipps-University Marburg
Faculty of Mathematics and Computer Science
(2009-2015)

Phone: +44 771O-19-249O
E-mail: kinzel @mathematik (.uni-marburg.de)

Area of research:

DFG-SPP 1324: Adaptive wavelet methods for stochastic partial differential equations

List of publications:

On the construction of stochastic fields with prescribed regularity by wavelet expansions,
Vietnam Journal of Mathematics (2017), 1-21
(with S. Dahlke and N. Döhring)
[DOI: 10.1007/s10013-017-0258-7]
On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs,
Potential Analysis 44 (2016), 473-495
(with P.A. Cioica, S. Dahlke, N. Döhring, U. Friedrich, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[DOI: 10.1007/s11118-015-9510-5], [preprint]
A class of random functions in non-standard smoothness spaces,
DFG-Priority Program 1324 Preprint No. 169, 2014
(with S. Dahlke and N. Döhring)
[preprint]
Adaptive wavelet methods for SPDEs (refereed)
In: Extraction of quantifiable information from complex systems, S. Dahlke, W. Dahmen, M. Griebel, W. Hackbusch, K. Ritter, R. Schneider, C. Schwab, and H. Yserentant (Eds.),
Lecture Notes in Computational Science and Engineering 102, Springer, 2014, 83-107
(with P.A. Cioica, S. Dahlke, N. Döhring, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[DOI: 10.1007/978-3-319-08159-5_5]
Convergence analysis of spatially adaptive Rothe methods,
Foundations of Computational Mathematics 14 (2014), 863-912
(with P.A. Cioica, S. Dahlke, N. Döhring, U. Friedrich, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[DOI: 10.1007/s10208-013-9183-7]
On the convergence analysis of Rothe's method,
DFG-Priority Program 1324 Preprint No. 124, 2012
(with P.A. Cioica, S. Dahlke, N. Döhring, U. Friedrich, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[preprint]
Adaptive wavelet methods for the stochastic Poisson equation,
BIT Numerical Mathematics 52 (2012), 589-614
(with P.A. Cioica, S. Dahlke, N. Döhring, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[DOI: 10.1007/s10543-011-0368-7], [preprint]
Spatial Besov regularity for stochastic partial differential equations on Lipschitz domains,
Studia Mathematica 207 (2011), 197-234
(with P.A. Cioica, S. Dahlke, F. Lindner, T. Raasch, K. Ritter, and R.L. Schilling)
[DOI: 10.4064/sm207-3-1], [preprint]

PhD thesis, Master thesis (see German designations):

Adaptive wavelet methods for a class of stochastic partial differential equations, Philips University Marburg (2015)
Gagliardo-Nirenberg Ungleichungen in diskreten Besov Räumen, Friedrich Schiller University Jena, Prof. Dr. W. Sickel (2007)

Presentations (selection):

Random wavelet expansions in anisotropic Besov spaces,
DFG-Priority Program 1324 5th annual meeting, Eisenach, December 2013
On the convergence analysis of spatially adaptive Rothe methods,
DFG-Priority Program 1324 4th annual meeting, Eisenach, November 2012
An abstract framework for the convergence analysis of Rothe's method for parabolic evolution equations,
Modern methods of time-frequency analysis II, Wavelet methods in scientific computing, Erwin Schrödinger International Institute for Mathematical Physics, Vienna, November 2012
Non-uniform discretization for the approximation of specific stochastic PDEs,
21st Rhein-Ruhr-Workshop, Königswinter, February 2011
Adaptive Wavelet methods for SPDEs: Non-uniform discretization for approximation of elliptic stochastic PDE,
DFG-Priority Program 1324 2nd annual meeting, Eisenach, October 2010
Numerical experiments for adaptive Wavelet methods for stochastic Poisson equations,
4th Workshop on Numerical analysis of stochastic PDEs, TU Bergakademie Freiberg, September 2010

Poster:

Adaptive wavelet methods for stochastic partial differential equations,
DFG-Priority Program 1324 Assessment colloquium, Frankfurt, May 2011
(with S. Dahlke, N. Döhring, F. Lindner, K. Ritter, and R.L. Schilling)
[pdf]
Selbstähnliche Pflasterungen (Self-similar Tilings),
Campus Marburg, November 2013
(AG Numerik, S. Dahlke, B. Schmitt)
[pdf]

Colloquia/Workshops attended:

New Discretization Methods for the Numerical Approximation of PDEs,
Mathematisches Forschungsinstitut Oberwolfach, January 2015
DFG-Priority Program 1324 Final conference,
Marburg, November 2014
DFG-Priority Program 1324 5th annual meeting,
Eisenach, December 2013
Workhop on high-performance computing Hessen,
TU Darmstadt, April 2013
DFG-Priority Program 1324 4th annual meeting,
Eisenach, November 2012
Modern methods of time-frequency analysis II, Wavelet methods in scientific computing,
Erwin Schrödinger International Institute for Mathematical Physics, Vienna, November 2012
Workshop on computational stochastics,
Annweiler am Trifels, March 2012
DFG-Priority Program 1324 3rd annual meeting,
Eisenach, November 2011
Workshop on rough paths and numerical integration methods,
Philipps-University Marburg, September 2011
21st Rhein-Ruhr-Workshop,
Königswinter, February 2011
DFG-Priority Program 1324 2nd annual meeting,
Eisenach, October 2010
4th Workshop on Numerical analysis of stochastic PDEs,
TU Bergakademie Freiberg, September 2010
Satellite summer school on Lévy processes: Theory and applications,
TU Braunschweig, July 2010
Workshop on nonlinear approximation,
Philipps-University Marburg, May 2010
DFG-Priority Program 1324 Annual meeting,
Zuse Institute Berlin, November 2009
Summer school on theoretical foundations and numerical methods for sparse recovery,
Johann Radon Institute for Computational and Applied Mathematics, Linz, August/September 2009
Workshop on stochastic partial differential equations: Modeling, analysis, and approximation,
TU Darmstadt, August 2009

Organization of colloquia/workshops/priority programme:

DFG-SPP 1324 Final conference
Marburg, November 2014
(assistance)
DFG-Priority Program 1324 5th annual meeting
Eisenach, December 2013
(with Frank Eckhardt and Stephan Dahlke)
Coordination of DFG-Priority Program 1324:
Mathematical methods for extracting quantifiable information from complex systems,
October 2011 - October 2012
(assistant to Prof. Dr. Stephan Dahlke)
Workshop: A computational approach to harmonic analysis
Philipps-Universität Marburg, August 2011
(assistance)
2nd - 4th DFG-Priority Program 1324 annual meetings
Eisenach, October 2010, November 2011, November 2012
(assistance)
Workshop on nonlinear approximation
Philipps-University Marburg, May 2010
(with Ulrich Friedrich and Stephan Dahlke)

Supervision:

SS 2014 Oberseminar zur Numerik,
Prof. Dr. Stephan Dahlke, Prof. Dr. Bernhard Schmitt
WS 2013/2014 Oberseminar zur Numerik
Prof. Dr. Stephan Dahlke, Prof. Dr. Bernhard Schmitt
SS 2013 Oberseminar zur Numerik,
Prof. Dr. Stephan Dahlke, Prof. Dr. Bernhard Schmitt
WS 2012/2013 Oberseminar zur Numerik,
Prof. Dr. Stephan Dahlke, Prof. Dr. Bernhard Schmitt
SS 2012 Oberseminar zur Numerik und Optimierung,
Prof. Dr. Stephan Dahlke, Prof. Dr. Ekatarina Kostina, Prof. Dr. Bernhard Schmitt
WS 2011/2012 Oberseminar zur Numerik und Optimierung,
Prof. Dr. Stephan Dahlke, Prof. Dr. Ekatarina Kostina, Prof. Dr. Bernhard Schmitt
WS 2010/2011 Oberseminar zur Numerik und Stochastik,
Prof. Dr. Stephan Dahlke, Prof. Dr. Steffen Dereich, Prof. Dr. Bernhard Schmitt
SS 2010 Oberseminar zur Numerik und Optimierung,
Prof. Dr. Ekatarina Kostina, Prof. Dr. Bernhard Schmitt
WS 2009/2010 Adaptive numerical methods for operator equations (in German),
Prof. Dr. Stephan Dahlke

Supervised theses:

Construction of random functions in Besov spaces based on wavelet expansions (in German),
Bachelor thesis by Alexander Sieber (2014),
Philipps-University Marburg, Prof. Dr. Stephan Dahlke
On the construction and theory of divergence-free wavelet bases (in German),
Diploma thesis by Xiaoyin Chen (2014),
Philipps-University Marburg, Prof. Dr. Stephan Dahlke
Analysis and implementation of divergence-free wavelet bases (in German),
Diploma thesis by Lufeng Yan (2013),
Philipps-University Marburg, Prof. Dr. Stephan Dahlke
Adaptive approximation of real-valued functions (in German),
Bachelor thesis by Philipp Werth (2011),
Philipps-University Marburg, Prof. Dr. Stephan Dahlke

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