Recent preprints

• With Harald Monsuur, Ultra-weak least squares discretizations for unique continuation and Cauchy problems, July 2024, arXiv:2407.04571v1.
  
  

Journal papers

• With Gregor Gantner, Improved rates for a space-time FOSLS of parabolic PDEs, September 2022, arXiv:2208.10824. Numer. Math. (2023) doi:10.1007/s00211-023-01387-3
  
  
• With Harald Monsuur, A pollution-free ultra-weak FOSLS discretization of the Helmholtz equation, March 2023, arXiv:2303.16508. Comput. Math. Appl. 148(4), 241--255 (2023) doi:10.1016/j.camwa.2023.08.013
  
  
• A convenient inclusion of inhomogeneous boundary conditions in minimal residual methods, Comput. Methods Appl. Math. (2023) doi:10.1515/cmam-2023-0072
  
  
• With Harald Monsuur, and Johannes Storn, Minimal residual methods in negative or fractional Sobolev norms, Math. Comp. (2023) doi:10.1090/mcom/3904
  
  
• With Johannes Storn, Interpolation Operators for parabolic Problems, Numer. Math (2023) doi:10.1007/s00211-023-01373-9
  
  
• With Wolfgang Dahmen and Harald Monsuur, Least squares solvers for ill-posed PDEs that are conditionally stable, ESAIM: M2AN 57(4), 2227-2255 (2023) doi:10.1051/m2an/202305
  
  
• With Gregor Gantner, Applications of a space-time FOSLS formulation for parabolic PDEs, IMA J. Numer. Anal. (2023) doi:10.1093/imanum/drad012
  
  
• With Gregor Gantner, A well-posed First Order System Least Squares formulation of the instationary Stokes equations. SIAM J. Numer. Anal. 60(3), 1607-1629 (2022) doi:10.1137/21M1432600
  
  
• With Raymond van Venetië and Jan Westerdiep, A wavelet-in-time, finite element-in-space adaptive method for parabolic evolution equations. Adv. Comput. Math., 2022. doi:10.1007/s10444-022-09930-w
  
  
• With Udo Boehm, Gregor Gantner, and Sonja Cox, Efficient numerical approximation of a non-regular Fokker-Planck equation associated with first-passage time distributions. BIT Numerical Mathematics, 2022. doi:10.1007/s10543-022-00914-2
  
  
• With Joost H. J. van Erp, Tom P. C. Schlösser, Ariënne W. Baijense, Thom E. Snijders,Willem Paul Gielis, René M. Castelein, Harrie Weinans, and Arthur de Gast, Calculation of the 3‐D femoral component’s orientation in total hip arthroplasty using. Sci Rep 12, 3499 (2022). doi:10.1038/s41598-022-07331-z
  
  
• With Wolfgang Dahmen, and Jan Westerdiep, Accuracy controlled data assimilation for parabolic problems. Math. Comp. 91 557-595 (2022). doi:10.1090/mcom/3680
  
  
• With Udo Boehm, Gregor Gantner, and Sonja Cox, Fast Solutions for the First-Passage Distribution of Diffusion Models with Space-Time-Dependent Drift Functions and Time-Dependent Boundaries. J. Math. Psychol. 105 (2021). 10.1016/j.jmp.2021.102613
  
  
• With Raymond van Venetië, Operator preconditioning: the simplest case. Appl. Numer. Math. 172, 292--299 (2022). doi:10.1016/j.apnum.2021.09.016
  
  
• With Giuseppe Carere, Maria Strazzullo, Francesco Ballarin, and Gianluigi Rozza, A weighted POD-reduction approach for parametrized PDE-constrained Optimal Control Problems with random inputs and applications to environmental sciences. Comput. Math. Appl. 102, 261--276 (2021). doi:10.1016/j.camwa.2021.10.020
  
  
• With Jan Westerdiep, Minimal residual space-time discretizations of parabolic equations: Asymmetric spatial operators. Comput. Math. Appl. 101, 107-118 (2021). doi:10.1016/j.camwa.2021.09.014 (A much better readable version can be found at https://arxiv.org/abs/2106.01090)
  
  
• With Thom E. Snijders, Tom P.C. Schlösser, Nathanael D Heckmann, Taro Tezuka, Rene M. Castelein, Harry Weinans, Arthur de Gast, Lawrence D. Dorr, The Effect of Functional Pelvic Tilt on the Three-Dimensional Acetabular Cup Orientation in Total Hip Arthroplasty Dislocations. J. Arthroplasty (2021). doi: 10.1016/j.arth.2020.12.055
  
  
• With Gregor Gantner, Further results on a space-time FOSLS formulation of parabolic PDEs. ESAIM: Mathematical Modelling and Numerical Analysis (2020). doi:10.1051/m2an/2020084
  
  
• With Raymond van Venetië, Uniform preconditioners of linear complexity for problems of negative order. Comput. Methods Appl. Math., (2020). doi:10.1515/cmam-2020-0052
  
  
• With Thom E. Snijders, Tom P.C. Schlösser, Maartje van Stralen, Renee M. Castelein, Harrie Weinans, Arthur de Gast, The Effect of Postural Pelvic Dynamics on the Three-dimensional Orientation of the Acetabular Cup in THA is Patient Specific. Clinical Orthopaedics and Related Research (2020). doi: 10.1097/CORR.0000000000001489
  
  
• With Raymond van Venetië, Uniform preconditioners for problems of positive order. Comput. Math. Appl. (2020). doi: 10.1016/j.camwa.2020.02.009
  
  
• With Jan Westerdiep, Stability of Galerkin discretizations of a mixed space-time variational formulation of parabolic evolution equations, IMA J. Numer. Anal. 41(1), (2021), doi:10.1093/imanum/drz069
  
  
• With Wolfgang Dahmen, Adaptive Strategies for Transport Equations. Comput. Methods Appl. Math. 19(3), (2019). doi:10.1515/cmam-2018-0230
  
  
• With Raymond van Venetië, Uniform preconditioners for problems of negative order, Math. Comp. (2019). doi: 10.1090/mcom/3481
  
  
• With Claudio Canuto, Ricardo H. Nochetto, and Marco Verani, A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square, ESAIM: Mathematical Modelling and Numerical Analysis (2019). doi: 10.1051/m2an/2019015
  
  
• With Stefano Berrone, Andrea Bonito, and Marco Verani, An optimal adaptive Fictitious Domain Method, Math. Comp. (2019). doi: 10.1090/mcom/3414
  
  
• With Nikolaos Rekatsinas, An optimal adaptive tensor product wavelet solver of a space-time FOSLS formulation of parabolic evolution problems, Adv. Comput. Math. (2018). doi: 10.1007/s10444-018-9644-2
  
  
• With Nikolaos Rekatsinas, A quadratic finite element wavelet Riesz basis, Int. J. Wavelets Multiresolut. Inf. Process. (2018). doi: 10.1142/S0219691318500339
  
  
• With Nikolaos Rekatsinas, An optimal adaptive wavelet method for first order system least squares, Numer. Math. 140(1), 191-237 (2018). doi: 10.1007/s00211-018-0961-7
  
  
• With Nabi Godarzvand Chegini, Adaptive piecewise tensor product wavelets scheme for Laplace-interface problems, J. Comput. Appl. Math. 336, 72-97 (2018). doi: 10.1016/j.cam.2017.12.021
  
  
• With Dirk Broersen, and Wolfgang Dahmen, On the stability of DPG formulations of transport equations, Math. Comp. (2017). doi: 10.1090/mcom/3242
  
  
• With Christoph Schwab, Fractional space-time variational formulations of (Navier-) Stokes equations, SIAM J. Math. Anal. 49(4), 2442-2467 (2017). doi: 10.1137/15M1051725
  
  
• With Claudio Canuto, Ricardo H. Nochetto, and Marco Verani, On p-Robust Saturation for hp-AFEM, Comput. Math. Appl. (2017) doi: 10.1016/j.camwa.2017.02.035
  
  
• With Claudio Canuto, Ricardo H. Nochetto, and Marco Verani, Adaptive Spectral Galerkin Methods with Dynamic Marking, SINUM 54(6), (2016). doi: 10.1137/15M104579X
  
  
• With Claudio Canuto, Ricardo H. Nochetto, and Marco Verani, Convergence and Optimality of hp-AFEM, Numer. Math. (2016). doi:10.1007/s00211-016-0826-x
  
  
• With Stephan Dahlke, Dominik Lellek, and Shiu Hong Lui, Adaptive Wavelet Schwarz Methods for the Navier-Stokes Equation, Numerical Functional Analysis and Optimization, Published online: 01 Jul 2016, DOI: 10.1080/01630563.2016.1198916
  
  
• Divergence-free wavelets on the hypercube: General boundary conditions, Constr. Approx., 1-35 (2016) DOI 10.1007/s00365-016-9325-7
  
  
• With Nabi Godarzvand Chegini, An adaptive wavelet method for semi-linear first order system least squares, Comput. Math. Appl., ISSN (Online) 1609-9389, ISSN (Print) 1609-4840, 10.1515/cmam-2015-0023, August 2015
  
  
• With Lars Diening, and Christian Kreuzer, Instance optimality of the adaptive maximum strategy, Found. Comput. Math. 16(1), 33-68 (2016). DOI 10.1007/s10208-014-9236-6
  
  
• With Dirk Broersen, A Petrov-Galerkin discretization with optimal test space of a mild-weak formulation of convection-diffusion equations in mixed form, IMA J. Numer. Anal. 35(1), 39-73 (2015). doi: 10.1093/imanum/dru003
  
  
• With Dirk Broersen, A robust Petrov-Galerkin discretisation of convection-diffusions equations, Comput. Math. Appl. 68(11), 1605–1618 (2014). doi:10.1016/j.camwa.2014.06.019
  
  
• With Dietmar Gallistl, Mira Schedensack, A remark on newest-vertex bisection in any space dimension, Comput. Methods Appl. Math. 14(3), 317–320 (2014). doi:10.1515/cmam-2014-0013
  
  
• With Rafaela Guberovic, and Christoph Schwab, Space-Time Variational Saddle Point Formulations of Stokes and Navier-Stokes Equations, ESAIM Math. Model. Numer. Anal. 48(3), 875-894 (2014). doi: 10.1051/m2an/2013124
  
  
• Adaptive wavelet methods for linear and nonlinear least squares problems, Found. Comput. Math. 14(2), 237-283 (2014). doi: 10.1007%2Fs10208-013-9184-6
  
  
• With Sebastian Kestler, Fast evaluation of system matrices w.r.t. multi-tree collections of tensor product refinable basis functions, J. Comput. Appl. Math. 260, 103-116 (2014). doi: 10.1016/j.cam.2013.09.015
  
  
• First Order System Least Squares with inhomogeneous boundary conditions, IMA J. Numer. Anal. 34(3), 863-878 (2014). doi: 10.1093/imanum/drt042
  
  
• With Nabi Godarzvand Chegini, Stephan Dahlke, and Ulrich Friedrich, Piecewise tensor product wavelet bases by extensions and approximation rates. Math. Comp. 82, 2157-2190 (2013). doi: 10.1090/S0025-5718-2013-02694-4
  
  
• With Sebastian Kestler, An efficient approximate residual evaluation in the adaptive tensor product wavelet method, J. Sci. Comput. 57(3), 439-463 (2013). doi: 10.1007/s10915-013-9712-1
  
  
• 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

• With N. Chegini, S. Dahlke, and U. Friedrich, Piecewise Tensor Product Wavelet Bases by Extensions and Approximation Rates. In: Extraction of Quantifiable Information from Complex Systems, Series: Lecture Notes in Computational Science and Engineering, Vol. 102, Dahlke, S., Dahmen, W., Griebel, M., Hackbusch, W., Ritter, K., Schneider, R., Schwab, C., Yserentant, H. (Eds.), Springer, 2014, 69-81.
  
  
• 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 Claudio Canuto, Ricardo H. Nochetto, and Marco Verani, High-Order Adaptive Galerkin Methods, In: Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Selected papers from the ICOSAHOM conference, June 23-27, 2014, Salt Lake City, Utah, USA Kirby, Robert M., Berzins, Martin, Hesthaven, Jan S. (Eds.), Springer 2015, 51-72.
  
  
• 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.