Workgroup Numerics

Dr. Ulrich Friedrich

Philipps-Universität Marburg
Faculty of Mathematics and Computer Science
Workgroup Numerics and Wavelet-Analysis
Hans-Meerwein-Str.
Lahnberge
35032 Marburg
Germany

Fax: +49(0)6421/28-26945
E-mail: friedrich@mathematik (.uni-marburg.de)

Research interests

  • DFG-SPP 1324 Project: Adaptive wavelet frame methods for operator equations: Sparse grids, vector-valued spaces and applications to nonlinear inverse parabolic problems
  • Adaptive wavelet methods for inverse problems: Acceleration Strategies, adaptive Rothe Method and generalized tensor wavelets

Publications

Papers

  • On the convergence analysis of the inexact linearly implicit Euler scheme for a class of SPDEs
    (with P.A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
    To appear in: Potential Anal.
    [Preprint] [arXiv]

  • Convergence analysis of spatially adaptive Rothe methods
    (with P.A. Cioica, S. Dahlke, N. Döhring, S. Kinzel, F. Lindner, T. Raasch, K. Ritter, R.L. Schilling)
    Foundations of Computational Mathematics 14 (5) (2014) 863--912. DOI: 10.1007/s10208-013-9183-7
    [Preprint] [Journal]

  • Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
    (with S. Dahlke, M. Fornasier, T. Raasch)
    Journal of Inverse and Ill-Posed Problems 23 (4) (2015) 393--414. DOI: 10.1515/jiip-2014-0031
    [Preprint] [Journal]

  • Piecewise tensor product wavelet bases by extensions and approximation rates
    (with N. Chegini, S. Dahlke, R. Stevenson)
    Mathematics of Computation 82 (2013) 2157--2190. DOI: 10.1090/S0025-5718-2013-02694-4
    [Preprint] [Journal]

  • An adaptive wavelet solver for a nonlinear parameter identification problem for a parabolic differential equation with sparsity constraints
    (with S. Dahlke, P. Maass, T. Raasch, R.A. Ressel)
    Journal of Inverse and Ill-Posed Problems 20 (2) (2012) 213--251. DOI: 10.1515/jip-2012-0013
    [Preprint] [Journal]

  • A two parameter generalization of Lions' nonoverlapping domain decomposition method for linear elliptic PDEs
    DFG-SPP 1324 Preprint 9, Philipps-Universität Marburg, 2009.
    [Preprint]

Book chapters (refereed)

  • Piecewise tensor product wavelet bases by extensions and approximation rates
    (with N. Chegini, S. Dahlke, R. Stevenson)
    In: Extraction of Quantifiable Information from Complex Systems
    (S. Dahlke, W. Dahmen, M. Griebel, W. Hackbusch, K. Ritter, R. Schneider, C. Schwab, H. Yserentant, Hrsg.)
    Lecture Notes in Computational Science and Engineering, vol. 102, Springer, 2014, pp. 83--107. DOI: 10.1007/978-3-319-08159-5_4
    [Kapitel] [Buch]

PhD thesis


Conference organization (as official organizer)


Teaching