Holger Wendland's
Publications

Check out my citation index.

Books

numerische Mathematik Numerische Mathematik (with Robert Schaback), Springer Lehrbuch, Springer, Berlin, Heidelberg, 2004.
 
scattered data approximation Scattered Data Approximation, Cambridge Monographs on Applied and Computational Mathematics, Cambridge University Press, Cambridge, 2005.

Papers

    Preprints

  1. (with Q. Thong Le Gia and Ian H. Sloan) A multiscale analysis in Sobolev spaces on the sphere, Preprint Sydney/Sussex 2009.
  2. (with Jochen Krebs and Alfred K. Louis) Sobolev error estimates and a priori parameter selection for semi-discrete Tikhonov regularization, Preprint Sussex/Saarbrücken 2008.
  3. (with Daniela Schräder) A high-order, analytically divergence-free discretization method for Darcy's problem, Preprint Sussex 2008.
  4. (with Peter Giesl) Approximating the basin of attraction of time-periodic ODEs by meshless collocation of a Cauchy problem, Preprint Sussex 2008, to appear in: Discrete and Continuous Dynamical Systems, Supplements.
  5. Particle methods for transport equations on surfaces, Preprint Sussex 2008.
  6. Meshfree space-time discretization for parabolic problems, Preprint Sussex 2008.

    2009

  7. (with Ian H. Sloan) Inf-sup conditions for spherical polynomials and radial basis functions on spheres, Math. Comp.78 (2009), 1319-1331, (pdf-file).
  8. Divergence-free kernel methods for approximating the Stokes problem, SIAM Journal on Numerical Analysis 47 (2009), 3158-3179.
  9. (with Peter Giesl) Approximating the basin of attraction of time-periodic ODEs by meshless collocation, Discrete and Continuous Dynamical Systems, Series A, 25 (2009), 1249 - 1274.

    2008

  10. Hybrid methods for fluid-structure-interaction problems in Aeroelasticity, in: M. Griebel, M. A. Schweitzer (eds.) Meshfree Methods for Partial Differential Equations IV, 335-358, Springer, Berlin, 2008. (pdf-file).
  11. (with Markus Rütten and Thomas Alrutz) A Vortex axis and vortex core border grid adaptation algorithm, International Journal for Numerical Methods in Fluids 58 (2008), 1379-1405. (pdf-file).
  12. (with Nira Dyn and Armin Iske) Meshfree thinning of 3d point clouds, J. Foundations of Computational Mathematics 8 (2008), 409-425.

    13. 2007

  13. (with Peter Giesl) Meshless Collocation: Error estimates with application to dynamical systems, SIAM Journal on Numerical Analysis 45 (2007), 1723-1741. ( pdf-file.)
  14. On the stability of meshless symmetric collocation for boundary value problems, BIT Numerical Mathematics 47 (2007), 455-468. ( pdf-file.)
  15. (with Regine Ahrem and Armin Beckert) Recovering rotations in aeroelasticity, Journal of Fluid and Structures 23 (2007), 874-884.
  16. (with Francis J. Narcowich, Xinping Sun, and Joseph D. Ward) Direct and inverse Sobolev error estimates for scattered data interpolation via spherical basis functions, J. Foundations of Computational Mathematics 7 (2007), 369-390. ( pdf-file.)

    17. 2006

  17. Spatial coupling in Aeroelasticity by meshless kernel-based methods, in: P. Wesseling, E. Onate, J. Periaux (eds.), Proceedings to ECCOMAS CFD 2006, Egmond aan Zee, The Netherlands.
  18. (with Quoc Le Gia, Francis J. Narcowich, and Joseph D. Ward) Continuous and discrete least-squares approximation by basis functions on spheres, Journal of Approximation Theory 143 (2006), 124-133. (pdf-file.)
  19. (with Robert Schaback) Kernel techniques: From machine learning to meshless methods, Acta Numerica 15 (2006), 543-639. ( pdf-file.)
  20. (with Regine Ahrem and Armin Beckert) A meshless spatial coupling scheme for large-scale fluid-structure-interaction problems, Computer Modeling in Engineering and Sciences 12 (2006), 121-136. ( pdf-file.)
  21. (with Francis J. Narcowich and Joseph D. Ward) Sobolev error estimates and a Bernstein inequality for scattered data interpolation via radial basis functions, Constructive Approximation 24 (2006), 175--186. ( pdf-file.)

    22. 2005

  22. (with Regine Ahrem and Armin Beckert) A new multivariate interpolation method for large-scale spatial coupling problems in aeroelasticity, Conference Proceedings to the International Forum on Aeroelasticity and Structural Dynamics (IFASD), Munich 2005, DGLR-Bericht 2005-04, ISBN 3-932-182-43-X. (pdf-file. )
  23. (with Christian Rieger) Approximate interpolation with applications to selecting smoothing parameters, Numerische Mathematik 101 (2005), 643-662.(pdf-file. )
  24. Computational aspects of radial basis function approximation, in K. Jetter et al. (eds.) Topics in Multivariate Approximation and Interpolation , Elsevier B.V., 2005, 231-256. (pdf-file.)
  25. On the convergence of a general class of finite volume methods, SIAM J. Numerical Analysis 43 (2005), 987-1002, (pdf-file. )
  26. (with Stefano De Marchi and Robert Schaback) Near-optimal data-independent point locations for radial basis function interpolation, Advances in Computational Mathematics 23 (2005), 317-330.
  27. (with Francis J. Narcowich and Joseph D. Ward) Sobolev bounds on functions with scattered zeros, with applications to radial basis function surface fitting, Mathematics of Computation 74 (2005), 743-763. (zipped ps-file. )

    28. 2004

  28. Solving large generalized interpolation problems efficiently, in M. Neamtu, E. B. Saff (eds.), Advances in Constructive Approximation , Nashboro Press, Brentwood, TN, 2004. (zipped ps-file.)

    29. 2003

  29. Reconstructing multivariate functions from large data sets, in W. Haussmann, K. Jetter, M. Reimer, Modern Developments in Multivariate Approximation, ISNM 145, Birkhäuser Verlag, Basel, 2003, 295-308.
  30. (with Francis J. Narcowich and Joseph D. Ward) Refined error estimates for radial basis function interpolation, Constructive Approximation 19 (2003), 541-564.

    31. 2002

  31. (with Robert Schaback) Approximation by positive definite kernels, in: M. D. Buhmann and D. H. Mache, Advanced Problems in Constructive Approximation, Birkhäuser Verlag, Basel, 2002, 203-221.
  32. Fast evaluation of radial basis functions: Methods based on partition of unity, in: C. K. Chui, L. L. Schumaker, and J. Stöckler (eds), Approximation Theory X: Wavelets, Splines, and Applications, Vanderbilt University Press, Nashville, 2002, 473-483. (zipped ps-file).
  33. (with Robert Schaback) Inverse and saturation theorems for radial basis function interpolation, Mathematics of Computation 71 (2002), 669-681. (zipped ps-file ).

    34. 2001

  34. Gaussian interpolation revisited, in: K. Kopotun, T. Lyche, and M. Neamtu (eds.), Trends in Approximation Theory , Vanderbilt University Press, Nashville, 2001, 427-436. (zipped ps-file. )
  35. Moving least squares approximation on the sphere, in: T. Lyche and L. L. Schumaker (eds.), Mathematical Methods in CAGD: Oslo 2000, Vanderbilt University Press, Nashville, 2001, 517-526. (zipped ps-file. )
  36. (with Armin Beckert) Multivariate interpolation for fluid-structure-interpolation problems using radial basis functions, Aerosp. Sci. Technol 5 (2001), 125-134. (pdf-file. )
  37. (with Robert Schaback) Characterization and construction of radial basis functions, in N. Dyn, D. Leviatan, D. Levin and A. Pinkus (eds), Multivariate Approximation and Applications , Cambridge University Press, Cambridge, 2001. (zipped ps-file. )
  38. Local polynomial reproduction and moving least squares approximation, IMA Journal of Numerical Analysis 21 (2001), 285-300. (zipped ps-file. )

    39. 2000

  39. (with Robert Schaback) Numerical Techniques based on radial basis functions, in A. Cohen, C. Rabut, and L. L. Schumaker (eds.), Curve and Surface Fitting: Saint-Malo 1999, 359-374, Vanderbilt University Press, Nashville, TN, 2000. (zipped ps-file. )
  40. (with Robert Schaback) Adaptive greedy techniques for approximate solution of large rbf systems, Numerical Algorithms 24 (2000), 239-254.(zipped ps-file. )
  41. Optimal approximation orders in Lp for radial basis functions, East Journal on Approximations 6 (2000), 87-102. (zipped ps-file ).

    42. before 2000

  42. (with Robert Schaback) Using compactly supported radial basis functions to solve partial differential equations, in: C.S. Chen, C.A. Brebbia and D.W. Pepper (eds.), Boundary Element Technology XIII, WitPress, Southampton, Boston, 1999, 311-324. (zipped ps-file. )
  43. On the smoothness of positive definite and radial functions, Journal of Computational and Applied Mathematics 101 (1999), 177-188. (zipped ps-file ).
  44. Meshless Galerkin methods using radial basis functions, Mathematics of Computation 68 (1999), 1521-1531. (zipped ps-file).
  45. Numerical solution of variational problems by radial basis functions, C. K. Chui and L. L. Schumaker (eds.), Approximation Theory IX, Volume 2: Computational Aspects, Vanderbilt University Press, Nashville, TN, 1998, 361-368. (zipped ps-file ).
  46. Error estimates for interpolation by compactly supported radial basis functions of minimal degree, Journal of Approximation Theory 93 (1998), 258-272. ( zipped ps-file).
  47. Sobolev-type error estimates for interpolation by radial basis functions, in: A. LeMéhauté, C. Rabut, and L.L. Schumaker (eds.), Surface Fitting and Multiresolution Methods , 337-344, Vanderbilt University Press, Nashville, TN, 1997. ( zipped ps-file).
  48. Piecewise polynomial, positive definite and compactly supported radial basis functions of minimal degree, Advances in Computational Mathematics 4 (1995), 389-396. ( zipped ps-file).