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Selected Publications

  • K. Höllig, Approximationszahlen von Sobolev-Einbettungen, Math. Annalen 242 (1979), 273-281.
  • C. de Boor, R. DeVore and K. Höllig, Mixed norm n-width, Proc. Amer. Math. Soc. 80 (1980), 577-583.
  • C. de Boor and K. Höllig, Recurrence relations for multivariate B-splines, Proc. Amer. Math. Soc. 85 (1982), 397-399.
  • K. Höllig, Existence of infinitely many solutions for a forward-backward heat equation, Trans. Amer. Math. Soc. 278 (1983), 299-316.
  • C. de Boor and K. Höllig, Approximation order from bivariate C1-cubics: A counterexample, Proc. Amer. Math. Soc. 87 (1983), 649-655.
  • K. Höllig and J. Nohel, A nonlinear integral equation occuring in a singular free boundary problem, Trans. Amer. Math. Soc. 283 (1984), 145-155.
  • C. de Boor, K. Höllig and S.D. Riemenschneider, Convergence of bivariate cardinal interpolation, Constructive Approximation 1 (1985), 183-193.
  • K. Höllig and H.-O. Kreiss, C infinity-regularity for the porous medium equation, Mathematische Zeitschrift 192 (1986), 217-224.
  • C. de Boor, K. Höllig and S.D. Riemenschneider, Convergence of cardinal series, Proc. Amer. Math. Soc. 98 (1986), 457-460.
  • K. Höllig, Geometric continuity of spline curves and surfaces, Lecture notes, ACM SIGGRAPH '86, Dallas, 1986.
  • A. Friedman and K. Höllig, On the Mesa Problem, J. Math. Anal. Appl. 123 (1987), 564-571.
  • K. Höllig and C.A. Micchelli, Divided differences, hyperbolic equations and lifting of distributions, Constructive Approximation 3 (1987), 143-156.
  • C. de Boor, K. Höllig and M. Sabin, High accuracy geometric Hermite interpolation, Computer-Aided Geometric Design 4 (1987), 269-278.
  • C. de Boor, K. Höllig and S. Riemenschneider, Fundamental solutions for multivariate difference equations, Amer. Math. J. 111 (1989), 403-415.
  • K. Höllig and C. de Boor, Box-spline tilings, Amer. Math. Monthly 98 (1991), 793-802.
  • K. Höllig and J. Koch, Geometric Hermite interpolation with maximal order and smoothness. CAGD 13 (1996), 681-695.
  • K. Höllig, Stability of the B-spline basis via knot insertion. CAGD 17(5) (2000), 447-450.
  • K. Höllig, U. Reif and J. Wipper, Weighted extended B-spline approximation of Dirichlet problems. SIAM Journal on Numerical Analysis 39(2) (2001), 442-462.
  • K. Höllig, U. Reif, J. Wipper, Multigrid methods with web-splines. Numerische Mathematik 91(2) (2002), 237-256.
  • K. Höllig, Finite Element Approximation with Splines. In: Handbook of Computer Aided Geometric Design. G. Farin, J. Hoschek, and M.S. Kim (eds.), Elsevier (2002), 283-308
  • K. Höllig, U. Reif, Nonuniform Web-Splines. Computer Aided Geometric Design 20 (2003), 277-294.
  • K. Höllig, C. Apprich, A. Streit, Introduction to the web-method and its applications. Advances in Computational Mathematics, Volume 23 (2005), pp. 215-237.
  • K. Höllig, J. Hörner and M. Pfeil, Parallel Finite Element Methods with Weighted Linear B-Splines. High Performance Computing in Science and Engineering '07, eds. W.E. Nagel, D. Kröner, and M. Resch, Springer (2008), 667-676.
  • K. Höllig, J. Hörner and A. Hoffacker, Finite Element Analysis with b-splines: weighted and isogeometric methods, in Curves and Surfaces 2010, LNCS 6920, Springer (2012), 330-350
  • C. Apprich, K. Höllig, J. Hörner, A. Keller and E. Nava Yazdani, Finite Element Approximation with Hierarchical B-Splines, in Curves and Surfaces 2014, LNCS 9213, Springer (2015), 1-15
  • K. Höllig and J. Hörner, Programming finite element methods with weighted B-splines, Computers & Mathematics with Applications 70(7), 1441-1456 (2015)
  • C. Apprich, K. Höllig, J. Hörner, U. Reif: Collocation with WEB-Splines, Advances in Computational Mathematics (42-4), Springer (2016), 823-842
  • K. Höllig, J. Hörner: Aufgaben und Lösungen zur Höheren Mathematik, Springer-Spektrum, 2017
  • C. Apprich, A. Dieterich, K. Höllig, E. Nava-Yazdani: Cubic spline approximation of a circle with maximal smoothness and accuracy. Computer Aided Geometric Design 56 (2017), 1-3.