Jun.-Prof. Dr. Markus Weimar - Research & Publications


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Area of Research

  • (Theoretical) Numerical Analysis
  • Theory of Function Spaces
  • Adaptive Wavelet Algorithms
  • (Nonlinear) Approximation Theory
  • Regularity Theory for Operator Equations (Besov Regularity)
    • (Nonlinear) Partial Differential Equations
    • Boundary Integral Equations
Further interests:
  • High-dimensional Problems
  • Information-Based Complexity (IBC)
  • Multivariate Integration (Lattice Rules)
  • Discrepancy Theory
  • Applied Harmonic Analysis


Publications

Preprints:

  1. Besov regularity of solutions to the p-Poisson equation in the vicinity of a vertex of a polygonal domain (with C. Hartmann)
    Submitted for publication
    Preprint: Bericht Mathematik Nr. 2017-01 des Fachbereichs Mathematik und Informatik, Universität Marburg
    [ pdf ]

Articles and Book chapters (peer reviewed):

  1. Adaptive wavelet BEM for boundary integral equations: Theory and numerical experiments (with S. Dahlke, H. Harbrecht, and M. Utzinger)
    To appear in Numer. Funct. Anal. Optim. (2017)
    [ arXiv, doi ]

  2. Construction of quasi-Monte Carlo rules for multivariate integration in spaces of permutation-invariant functions (with D. Nuyens and G. Suryanarayana)
    Constr. Approx. 45(2) (2017), 311-344
    [ arXiv, doi ]

  3. Rank-1 lattice rules for multivariate integration in spaces of permutation-invariant functions: Error bounds and tractability (with D. Nuyens and G. Suryanarayana)
    Adv. Comput. Math. 42(1) (2016), 55-84
    [ arXiv, doi ]

  4. Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann, and B. Scharf)
    Nonlinear Anal. 130 (2016), 298-329
    [ arXiv, doi ]

  5. Almost diagonal matrices and Besov-type spaces based on wavelet expansions
    J. Fourier Anal. Appl. 22(2) (2016), 251-284
    [ arXiv, doi ]

  6. Notes on (s,t)-weak tractability: A refined classification of problems with (sub)exponential information complexity (with P. Siedlecki)
    J. Approx. Theory 200 (2015), 227–258
    [ arXiv, doi ]

  7. Besov regularity for operator equations on patchwise smooth manifolds (with S. Dahlke)
    J. Found. Comput. Math. 15(6) (2015), 1533-1569
    [ arXiv, doi ]

  8. Breaking the curse of dimensionality
    Dissertationes Math. 505 (2015), 112 pp.
    [ see No.2 in Theses, doi ]

  9. On lower bounds for integration of multivariate permutation-invariant functions
    J. Complexity 30(1) (2014), 87-97
    [ arXiv, doi ]

  10. Probabilistic star discrepancy bounds for double infinite random matrices (with C. Aistleitner)
    J. Dick, F.Y. Kuo, G.W. Peters, and I.H. Sloan (Eds.) - Monte Carlo and Quasi-Monte Carlo Methods 2012. Springer, Berlin, 2013, pp 271-287
    [ pdf, doi ]

  11. The complexity of linear tensor product problems in (anti)symmetric Hilbert spaces
    J. Approx. Theory 164(10) (2012), 1345-1368
    [ arXiv (extended version), doi ]

  12. Tractability results for weighted Banach spaces of smooth functions
    J. Complexity 28(1) (2012), 59-75
    [ pdf, doi ]

Reports and posters:

  1. Wavelet und Frame Techniken für BEM in der Akustik (with W. Kreuzer und T. Hrycak)
    Fortschritte der Akustik, DAGA 2016, 42. Jahrestagung für Akustik. Deutsche Gesellschaft für Akustik e.V., Aachen, 2016, pp 855-858.
    [ web ]

  2. (s,t)-weak tractability
    A. Hinrichs, J.F. Traub, H. Woźniakowski, and L. Yaroslavtseva (Eds.) - Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 15391). Dagstuhl Reports 5(9), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2016, p 74
    [ web, doi ]

  3. Besov regularity of solutions to the p-Poisson equation (with S. Dahlke, L. Diening, C. Hartmann, and B. Scharf)
    Poster (2014)
    [ pdf ]

  4. On lower bounds for integration of multivariate permutation-invariant functions
    M. Gnewuch, F.Y. Kuo, H. Niederreiter, and Woźniakowski, H. (Eds.) - Uniform Distribution Theory and Applications. Oberwolfach Reports 10(4), EMS Publishing House, Zürich, 2013, pp 2904-2905
    [ web, doi ]

  5. Probabilistic star discrepancy bounds for double infinite random matrices
    A. Keller, F.Y. Kuo, A. Neuenkirch, and J.F. Traub (Eds.) - Algorithms and Complexity for Continuous Problems (Dagstuhl Seminar 12391). Dagstuhl Reports 2(9), Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2013, p 223
    [ web, doi ]

Theses:

  1. Several Approaches to Break the Curse of Dimensionality
    Ph.D. thesis, Friedrich-Schiller-University Jena, 20/02/2013
    supervised by Prof. Dr. Erich Novak
    [ arXiv, urn ]

  2. Das Haar'sche System in Funktionenräumen vom Typ Asp,q(IR)
    Diploma thesis, Friedrich-Schiller-University Jena, 08/09/2009
    supervised by Prof. Dr. Hans-Jürgen Schmeißer and Prof. Dr. Dr. h.c. Hans Triebel
    [ pdf (abstract, german) ]

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