Recent preprints

• With Sebastian Kestler, Fast evaluation of system matrices w.r.t. multi-tree collections of tensor product refinable basis functions, 18 pages, March 2012. Submitted.
  
  
• A note on First Order System Least Squares (FOSLS) with inhomogeneous boundary conditions, 10 pages, February 2012. Submitted.
  
  
• Adaptive wavelet methods for linear and nonlinear least squares problems, 40 pages, November 2011. Submitted.
  
  
• With Rafaela Guberovic, and Christoph Schwab, Space-Time Variational Saddle Point Formulations of Stokes and Navier-Stokes Equations, 20 pages, December 2011. Submitted.
  
  
• With Nabi Godarzvand Chegini, Stephan Dahlke, and Ulrich Friedrich, Piecewise tensor product wavelet bases by extensions and approximation rates. Revised version, March 2012, 33 pages. Accepted for publication in Math. Comp.
  
  

Journal papers

• With Nabi Godarzvand Chegini, The adaptive tensor product wavelet scheme: Sparse matrices and the application to singularly perturbed problems, IMA J. Numer. Anal. 32(1), 75--104 (2012). doi: 10.1093/imanum/drr013
  
  
• With Christoph Schwab, Fast evaluation of nonlinear functionals of tensor product wavelet expansions, Numer. Math. 119(4), 765--786 (2011). doi: 10.1007/s00211-011-0397-9
  
  
• Divergence-free wavelet bases on the hypercube: Free-slip boundary conditions, and applications for solving the instationary Stokes equations, Math. Comp. 80, 1499-1523 (2011). doi: 10.1090/S0025-5718-2011-02471-3
  
  
• With Nabi Godarzvand Chegini, Adaptive wavelet schemes for parabolic problems: Sparse matrices and numerical results, SIAM J. Numer. Anal. 49(1), 182-212 (2011). doi:10.1137/100800555
  
  
• With Alan Demlow, Convergence and quasi-optimality of an adaptive finite element method for controlling L₂ errors, Numer. Math. 117(2), 185--218 (2011). doi:10.1007/s00211-010-0349-9
  
  
• Divergence-free wavelet bases on the hypercube, Appl. Comput. Harmon. Anal. 30, 1-19 (2011). doi:10.1016/j.acha.2010.01.007
  
  
• With Monique Dauge, Sparse tensor product wavelet approximation of singular functions, SIAM J. Math. Anal. 42(5), 2203-2228 (2010). doi:10.1137/090764694
  
  
• With Tammo Jan Dijkema, A sparse Laplacian in tensor product wavelet coordinates, Numer. Math. 115(3), 433-449 (2010). doi:10.1007/s00211-010-0288-5
  
  
• With Tammo Jan Dijkema and Christoph Schwab, An adaptive wavelet method for solving high-dimensional elliptic PDEs, Constr. Approx. 30(3), 423-455 (2009).
  
  
• With Hoang Nguyen, Finite element wavelets with improved quantitative properties, J. Comput. Appl. Math. 230(2), 706-727 (2009).
  
  
• With Christoph Schwab, Space-Time Adaptive Wavelet Methods for Parabolic Evolution Problems, Math. Comp.78, 1293-1318 (2009).
  
  
• With Mario Mommer, A goal-oriented adaptive finite element method with convergence rates, SIAM J. Numer. Anal. 47(2), 861-886 (2009). Extended preprint version.
  
  
• With Manuel Werner, A multiplicative Schwarz adaptive wavelet method for elliptic boundary value problems , Math. Comp.78, 619-644 (2009).
  
  
• With Yaroslav Kondratyuk, An optimal adaptive algorithm for the Stokes problem, SIAM J. Numer. Anal. 46(2), 747-775 (2008). Extended preprint version
  
  
• The completion of locally refined simplicial partitions created by bisection, Math. Comp.77, 227-241 (2008).
  
  
• With Christoph Schwab, Adaptive wavelet algorithms for Elliptic PDE's on product domains, Math. Comp.77, 71-92 (2008).
  
  
• More on the order of prolongations and restrictions, Appl. Numer. Math. 58, 1875-1880 (2008).
  
  
• With Manuel Werner, Computation of differential operators in aggregated wavelet frame coordinates, IMA J. Numer. Anal., 28(2): 354-381 (2008).
  
  
• With Stephan Dahlke, Massimo Fornasier, Thorsten Raasch, and Manuel Werner, Adaptive Frame Methods for Elliptic Operator Equations: The Steepest Descent Approach, IMA J. Numer. Anal., 27(4), 717-740 (2007).
  
  
• With Tsogtgerel Gantumur and Helmut Harbrecht, An optimal adaptive wavelet method without coarsening of the iterands, Math. Comp.76, 615-629 (2007).
  
  
• Composite wavelet bases with extended stability and cancellation properties, SIAM J. Numer. Anal. 45(1), 133-162 (2007). Extended preprint version.
  
  
• Optimality of a standard adaptive finite element method, Found. Comput. Math. 7(2), 245-269 (2007).
  
  
• With Helmut Harbrecht, Wavelets with patchwise cancellation properties, Math. Comp. 75, 1871-1889 (2006).
  
  
• With Tsogtgerel Gantumur, Computation of differential operators in wavelet coordinates, Math. Comp. 75, 697-709 (2006).
  
  
• With Tsogtgerel Gantumur, Computation of singular integral operators in wavelet coordinates, Computing, 76, 77-107 (2006).
  
  
• With Bishnu Lamichhane and Barbara Wohlmuth, Higher Order Mortar Finite Element Methods in 3D with Dual Lagrange Multiplier Bases, Numer. Math., 102(1), 93 - 121 (2005).
  
  
• An optimal adaptive finite element method, SIAM J. Numer. Anal., 42(5), 2188-2217 (2005).
  
  
• The uniform saturation property for a singularly perturbed reaction-diffusion equation, Numer. Math., 101(4), 355-379 (2005).
  
  
• With Oleg Davydov, Hierarchical Riesz bases for H^s(Ω), 1 < s < 5/2, Constr. Approx., 22(3), 365-394 (2005).
  
  
• On the compressibility of operators in wavelet coordinates, SIAM J. Math. Anal. 35(5), 1110-1132 (2004)
  
  
• Locally supported, piecewise polynomial biorthogonal wavelets on non-uniform meshes, Constr. Approx. 19(4), 477-508 (2003)
  
  
• Adaptive solution of operator equations using wavelet frames, SIAM J. Numer. Anal.41(3), 1074-1100 (2003)
  
  
• With Hoang Nguyen, Finite element wavelets on manifolds, IMA J. Numer. Math 23, 149-173 (2003)
  
  
• An analysis of nonconforming multi-grid methods, leading to an improved method for the Morley element, Math. Comp. 72, 55-81 (2003)
  
  
• A stable, direct solver for the gradient equation, Math. Comp. 72, 41-53 (2003)
  
  
• Nonconforming finite elements and the cascadic multi-grid method, Numer. Math. 91, 351-387 (2002)
  
  
• With Wolfgang Dahmen, Element-by-element contruction of wavelets satisfying stability and moment conditions, SIAM J. Numer. Anal. 37, 319-352 (1999)
  
  
• Stable Three-Point Wavelet Bases on General Meshes, Numer. Math. 80, 131-158 (1998)
  
  
• Experiments in 3D with a three-point hierarchical basis preconditioner, Appl. Numer. Math. 23, 159-176 (1997)
  
  
• A Robust Hierarchical Basis Preconditioner on General Meshes, Numer. Math. 78, 269-303 (1997)
  
  
• The Frequency Decomposition Multi-Level Method: A robust additive hierarchical basis preconditioner, Math. Comp. 65, 983-997 (1996)
  
  
• Robustness of the Additive and Multiplicative Frequency Decomposition Multi-Level Method, Computing 54, 331-346 (1995)
  
  
• Modified ILU as a smoother, Numer. Math. 68, 295-309 (1994)
  
  
• Robustness of Multi-Grid applied to Anisotropic Equations on Convex Domains and on Domains with Re-entrant Corners, Numer. Math. 66, 273-398 (1993)
  
  
• Discrete Sobolev Spaces and Regularity of Elliptic Difference Schemes RAIRO Modél. Math. Anal. Numér., 25, 607-640 (1991)
  
  

Book chapters

• Adaptive wavelet methods for solving operator equations: An overview. In: Multiscale, Nonlinear and Adaptive Approximation: Dedicated to Wolfgang Dahmen on the Occasion of his 60th Birthday, R.A. DeVore, A. Kunoth (eds.), Springer, 659 pages, September 2009, ISBN-10 / ASIN: 3642034128, ISBN-13 / EAN: 9783642034121, 543-594.
  
  
• Introduction to Multi-Grid. In: Numerical Methods for Advection-Diffusion Problems, C.B. Vreugdenhil en B. Koren (eds.), Vieweg Verlag, Braunschweig, 1993, 321-334.
  
  

Papers in conference proceedings

• With Jan Brandts, A stable and optimal complexity solution method for mixed finite element discretizations, Proceedings of EQUADIFF, 10 (Prague, 2001), Mathematica Bohemica 127(2), 153-161 (2002)
  
  
• Piecewise linear (pre-)wavelets on non-uniform meshes. In: Multigrid Methods V, W. Hackbusch and G. Wittum (eds.), Springer-Verlag, Heidelberg, 1996, 306-319.
  
  
• Robust Multi-Grid with 7-point ILU Smoothing. In: Multigrid Methods IV, P.W. Hemker and P. Wesseling (eds.), Birkhäuser, Basel, 1994, 295-308.
  
  
• New Estimates of the Contraction Number of V-cycle Multi-Grid with Applications to Anisotropic Equations. In: Incomplete Decompositions, W. Hackbusch and G. Wittum (eds.), Vieweg Verlag, Braunschweig, 1992, 607-640.
  
  

PhD Thesis

• On the Validity of Local Mode Analysis of Multi-Grid Methods, Utrecht University, December 1990
  
  

Other publications

• Construction of finite element wavelets on general domains or manifolds, Lecture notes C.I.M.E. Summerschool ``Multiscale Problems and Methods in Numerical Simulations'', September 9-15, 2001, Martina Franca, Italy.
  
  
• A stable, direct post-processing procedure to compute the pressure for the Stokes equations, University of Nijmegen, Report No. 9810, 15 pages, April 1998.
  
  
• The Cascade iteration for nonconforming discretizations, University of Nijmegen, Report No. 9803, 22 pages, February 1998.