Institut für Numerische Mathematik

Publications and Reports, Karsten Urban

 

If you are interested in one of the articles which -due to copyrights- are not available online, please email me.

Recent Preprints

  1. The Kolmogorov N-width for linear transport: Exact representation and the influence of the data, Florian Arbes, Constantin Greif and Karsten Urban, Universität Ulm (2023) submitted to ACOM
  2. An Ultra-Weak Space-Time Variational Formulation for the Schrödinger Equation, Stefan Hain and Karsten Urban, Universität Ulm (2022).

Published Lecture Notes and Monographs

  1. Michael Hinze, J. Nathan Kutz, Olga Mula, Karsten Urban: Model Order Reduction and Applications, Maurizio Falcone, Gianluigi Rozza (editors), Springer Cham, 2023
  2. Partial Differential Equations: An analytic and numerical approach - Wolfgang Arendt, Karsten Urban, translated from German by J. B. Kennedy,  Springer New York, Graduate Texts in Mathematics, 2023.
  3. Partielle Differenzialgleichungen: Eine Einführung in analytische und numerische Methoden (2. Auflage) - Wolfgang Arendt, Karsten Urban, Spektrum Akademischer Verlag (Springer) Heidelberg, 2018.
  4. Partielle Differenzialgleichungen: Eine Einführung in analytische und numerische Methoden - Wolfgang Arendt, Karsten Urban, Spektrum Akademischer Verlag (Springer) Heidelberg, 2010.
  5. Wavelet Methods for Elliptic Partial Differential Equations - Karsten Urban, Oxford University Press, 2009 (482 pages).
  6. Wavelets in Numerical Simulation: Problem Adapted Construction and Applications - Karsten Urban, Springer Lecture Notes in Computational Science and Engineering, Vol. 22, ISBN 3-540-43055-5, 2002
  7. Eine Einführung in C++" (in german) - Karsten Urban, Skripte im Shaker Verlag at Shaker Verlag, 1998, ISBN 3-8265-3749-1. Die Beispielprogramme findet man hier.

 

Refereed Papers in Books and Journals

 

  1. A Cerified Wavelet-Based Physics-Informed Neural Network for the Solution of Parametrized Partial Differential Equations, Lewin Ernst and Karsten Urban, accepted in IMA Journal of Numerical Analysis, 2024.
  2. The Reduced Basis Method in Space and Time: Challenges, Limits and Perspectives, Karsten Urban, in: Model Order Reduction and Application, Springer Lecture Notes in Mathematics 2023, 1-72.
  3. Multiskalenprobleme in der Numerik-Lehre - Ein Erfahrungsbericht, Laura Burr, Stefan Hain, Klaus Stolle, and Karsten Urban, in: Unterstützungsmaßnahmen in mathematikbezogenen Studiengängen, Reinhard Hochmuth, Rolf Biehler, Michael Liebendörfer, Niclas Schaper (Hrsg.), Springer Nature 2022, 471-490.
  4. A Space-Time Variational Method for Optimal Control Problems: Well-posedness, stability and numerical solution, Nina Beranek, M. Alexander Reinhold, Karsten Urban, Computational Optimization and Applications 2023. doi: 10.1007/s10589-023-00507-x
  5. An ultraweak space-time variational formulation for the wave equation: Analysis and efficient numerical solution, Julian Henning, Davide Palitta, Valeria Simoncini and Karsten Urban, ESAIM: M2AN 56 (4) 1173-1198 (2022)
    https://www.esaim-m2an.org/articles/m2an/abs/2022/04/m2an210138/m2an210138.html
  6. An Ultraweak Variational Method for Parametrized Linear Differential-Algebraic Equations,  Emil Beurer, Moritz Feuerle, Niklas Reich and Karsten Urban, Front. Appl. Math. Stat. 8:910786.
    doi: 10.3389/fams.2022.910786
    https://www.frontiersin.org/articles/10.3389/fams.2022.910786/full
  7. Linear/Ridge Expansions: Enhancing Linear Approximations by Ridge Functions Constantin Greif, Philipp Junk and Karsten Urban,  Adv. Comp. Math. 48:15 (2022).
  8. Simulating Metaphyseal Fracture Healing in the Distal Radius - Lucas Engelhardt, Frank Niemeyer, Patrick Christen, Ralph Müller, Kerstin Stock, Michael Blauth, Karsten Urban, Anita Ignatius, Ulrich Simon, Biomechanics 1 (2021), 29-42.
  9. A Variational Fomulation for LTI-Systems and Model Reduction Moritz Feuerle and Karsten Urban, in: Vermolen F.J., Vuik C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham, 1059-1067 (2021).
  10. Matrix oriented reduction of space-time Petrov-Galerkin variational problems Julian Henning, Davide Palitta, Valeria Simoncini and Karsten Urban, Universität Ulm (2019), in: Vermolen F.J., Vuik C. (eds) Numerical Mathematics and Advanced Applications ENUMATH 2019. Lecture Notes in Computational Science and Engineering, vol 139. Springer, Cham, 1049-1057 (2021).
  11. HT-AWGM: A Hierarchical Tucker-Adaptive Wavelet Galerking Method for High Dimensional Elliptic Problems Mazen Ali, Karsten Urban, Adv. Comp. Math. 46:59 (2020).
  12. Intraday Renewable Electricity Trading: Advanced Modeling and Numerical Optimal Control Silke Glas, Rüdiger Kiesel, Sven Kolkmann, Marcel Kremer, Nikolaus Graf von Luckner, Lars Ostmeier, Karsten Urban and Christoph Weber, in: J. Math. in Industry 10(3), https://rdcu.be/b1dJM (2020).
  13. Intraday Renewable Electricity Trading: Advanced Modeling and Optimal Control
    Silke Glas, Rüdiger Kiesel, Sven Kolkmann, Marcel Kremer, Nikolaus Graf von Luckner, Lars Ostmeier, Karsten Urban and Christoph Weber, in: Progress in Industrial Mathematics at ECMV 2018, I. Faragó, F. Izsák, P. L. Simon (eds.), 469-476, Springer 2019.
  14. A Reduced Basis Method for the Wave Equation
    Silke Glas, Anthony T. Patera and Karsten Urban, in: Int. J. Comput. Fluid Dyn. (2019), 1-8.
  15. Decay of the Kolmogorov N-width for wave problems
    Constantin Greif and Karsten Urban, Appl. Math. Lett. 96, 2019, 216-222.
  16. A Hierarchical A-Posteriori Error Estimator for the Reduced Basis Method Stefan Hain, Mario Ohlberger, Mladjan Radic, Karsten Urban, Ulm University  (2018) ArXiv No. 1082.03298.  Adv. Comp. Math., 45 (2019), 2191-2214.
  17. Modelling the Fracture-healing Process as a Moving-interface Problem using an Interface-capturing Approach Anita Ignatius, Frank Niemeyer, Martin Pietsch, Ulrich Simon, Karsten Urban, Computer Methods in Biomechanics and Biomedical Engineering, 21 (8), 512-520 (2018).
  18. (Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods
    Julia Brunken, Kathrin Smetana, Karsten Urban, in: SIAM Journal on Scientific Computing 41 (1), A592-A621 (2019).
  19. Two Ways to Treat Time in Reduced Basis Methods Silke Glas, Antonia Mayerhofer, Karsten Urban, in: Model Reduction of Parametrized Systems, P. Benner, M. Ohlberger, A. Patera, G. Rozza, K. Urban (eds.), Springer, 2017, 1-16.
  20. A Reduced Basis Method for Parameter Functions Using Wavelet Approximations Antonia Mayerhofer, Karsten Urban, in: Model Reduction of Parametrized Systems, P. Benner, M. Ohlberger, A. Patera, G. Rozza, K. Urban (eds.), Springer, 2017, 77-90.
  21. A Reduced Basis Method for the Hamilton-Jacobi-Bellmann Equation with Application to the European Union Emission Trading Scheme Sebastian Steck, Karsten Urban, to appear in: "Hamilton-Jacobi-Bellmann Equation. Numerical Methods and Applications in Optimal Control", de Gruyter 2017, 189-210.
  22. High performance computing on smartphones - Anthony T. Patera, Karsten UrbanSnapshots of modern mathematics from Oberwolfach, No 6/2016
  23. Reduced Basis Exact Error Estimates with Wavelets Mazen Ali, Karsten Urban, University of Ulm (2015). To appear in Proceedings of ENNUMATH 2015.
  24. Numerical Investigations of an Error Bound for Reduced Basis Approximations of Non-Coercice Variational Inequalities Silke Glas, Karsten Urban, IFAC-PapersOnLine 48-1, 721-726 (2015).
  25. A Reduced Basis Method for Parabolic Partial differential Equations with Parameter Functions and Applications to Option Pricing Antonia Mayerhofer, Karsten Urban, University of Ulm (2014), in Journal of Computational Finance (2016). (DOI 10.21314/JCF.2016.323)
  26. Maxwell's Equations with Impedance Boundary Conditions: Discontinuous Galerkin and Reduces Basis Methods  Kristin Kirchner, Karsten Urban, M2AN ESAIM: Mathematical Modelling and Numerical Analysis 50 (2016), 1763-1787. (DOI 10.1051/m2an/2016006)
  27. Adjoint-Based Optimization for Rigid Body Motion in Multiphase Navier-Stokes Flow Julia Spinger, Karsten Urban,  SIAM Journal on Scientific Computing, 37 (2), B185-B214 (2015). (DOI:10.1137/140974511)
  28. Reduced Basis Methods Based with Adaptive Snapshot Computations - Mazen Ali, Kristina Steih, Karsten Urban, University of Ulm (2014), accepted for publication in ACOM.Software for the numerical tests (zip-archive). Please Email me for receiving the password to open the archive.
  29. An Efficient Space-Time Adaptive Wavelet Galerkin Method for Time-Periodic Parabolic Partial Differential Equations - Sebastian Kestler, Karsten Urban, Kristina Steih,  Mathematics of Computation, online first (2015).
  30. Space-Time Reduced Basis Methods for Time-Periodic Parametric Differential Equations - Kristina Steih, Karsten Urban, preprint, University of Ulm (2012)
  31. Gerade weil die Vor- und  Nachbereitung enorm ist - Experteninterview zu Projektseminaren  - Karsten Urban, in: „Gute Hochschullehre: Eine evidenzbasierte Orientierungshilfe“, M. Schneider, M. Mustafic (Hrsg.), Springer-Verlag Berlin 2015, 73-87.
  32. On Non-Coercive Variational Inequalities - Silke Glas, Karsten Urban, in: SIAM Journal on Numerical Analysis,  52(5), 2250–2271, (2014), DOI:10.1137/130925438.
  33. Valuation of Structured Financial Products by Adaptive Multiwavelet Methods in High Dimensions - Rüdiger Kiesel, Andreas Rupp, Karsten Urban,  in: S. Dahlke et al. (eds.), Extraction of Quantifiable Information from Complex Systems, Lecture Notes in Computational Science and Engineering 102, Springer Switzerland (2014), Ch. 16, 279-303.
  34. Comparison of the EM Algorithm and Alternatives - Theresa Springer, Karsten Urban, University of Ulm (2012),  in: Numerical Algorithms, Volume 67, Issue 2 (2014), Page 335-364, DOI 10.1007/s11075-013-9794-8.
  35. Greedy Sampling using Nonlinear Optimization - Karsten Urban, Stefan Volkwein, Oliver Zeeb, in: Reduced Order Methods for Modeling and Computational Reductions, A. Quarteroni, G. Rozza (Eds.), Springer 2014, 139-157.
  36. On Wavelet-Galerkin Methods for Semilinear Parabolic Equations with Additive Noise - Mihály Kovács, Stig Larsson, Karsten Urban,  in: Monte Carlo and Quasi-Monte Carlo Methods 2012, J. Dick, F. Y. Kuo, G. W. Peters, I. H. Sloan (eds.), Springer 2014, 481-499.
  37. A Space-Time Certified Reduced Basis Method for Burgers' Equation - Masayuki Yano, Anthony T. Patera, Karsten Urban, in: Mathematical Models and Methods in Applied Sciences, Vol. 24, No. 9 (2014) 1903-1935. DOI: 10.1142/S0218202514500110
  38. An Improved Error Bound for Reduced Basis Approximation of Linear Parabolic Problems- Karsten Urban, Anthony T. Patera, Math. Comp. 2013, 50025-5718 (2013) 02782-2. 
  39. Reduced Basis Methods for Parameterized Partial Differential Equations with Stochastic Influences Using the Karhunen-Loève Expansion- Bernard Haasdonk, Karsten Urban, Bernhard Wieland, SIAM/ASA J. Uncert. Quant. 1 (2013), 79-105.
  40. Reduced Basis Methods for Quadratically Nonlinear Partial Differential Equations with Stochastic Influences- Karsten Urban, Bernhard Wieland, veröffentlicht in: CD-ROM Proceedings ECCOMAS 2012, Vienna, Austria
  41. Space-Time Reduced Basis Methods for Time-Periodic Partial Differential Equations -Kristina Steih, Karsten Urban, accepted for publication in Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, February 15-17, 2012
  42. Affine Decompositions of Parametric Stochastic Processes for Application within Reduced Basis Methods-Karsten Urban, Bernhard Wieland, accepted for publication in Proceedings of MATHMOD 2012 - 7th Vienna International Conference on Mathematical Modelling, Vienna, February 15-17, 2012
  43. A new error bound for Reduced Basis approximation of parabolic partial differential equations- Karsten Urban und Anthony T. Patera, CR Acad Sci Paris Series I, 350(3-4):203–207, 2012.
  44. Wavelet Methods for the representation, analysis and simulation of optical surfaces- Philipp Jester, Christoph Menke, Karsten Urban, IMA J Appl Math first published online July 22, 2011, 1-21 doi:10.1093/imamat/hxr030
  45. Adaptive Wavelet Methods on unbounded domains- Sebastian Kestler, Karsten Urban, J.Sci.Comp.,  Volume 53, Issue 2 (2012), Page 342-376
  46. Numerical Modelling and Simulation of Ship Hull Geometries- Michael Hopfensitz, Juan C. Matutat, Karsten Urban, in: Progress in Industrial Mathematics at ECMI 2010, M. Günther, A. Bartel, M. Brunk, S. Schöps. U. Striebel (Eds.), Mathematics in Industry Vol 17, Springer 2012, 465-472.
  47. A B-Spline Representation of Optical Surfaces and its Accuracy in a Ray Trace Algorithm- Philipp Jester, Christoph Menke, Karsten Urban, Applied Optics, Vol 50, p.822-828 (2011).
  48. Comparison of the Reduced-Basis and POD a-Posteriori Error Estimators for an Elliptic Linear-Quadratic Optimal Control Problem- Timo Tonn, Karsten Urban, Stefan Volkwein, Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences, Vol. 17 (4), 355-369 (2011).
  49. Automatic Differentiation for the Optimization of a Ship Propulsion and Steering System- Ralf Leidenberger, Karsten Urban, J. Glob. Optim. 10-1641 (online first), 2010.
  50. A coupled pressure based solution algorithm based on the volume-of-fluid approacg for two and more immiscible fluids- Kathrin Kissling, Julia Springer, Hrvoje Jasak, Steffen Schütz, Karsten Urban, Manfred Piesche, Proceedings of the V European Conference on Computational Fluid Dynamics ECCOMAS CFD 2010 J. C. F. Pereira, A. Sequeira and J. M. C. Pereira (Eds) Lisbon, Portugal,14-17 June 2010.
  51. Optimal Control of Parameter-Dependent Convection-Diffusion Problems Around Rigid Bodies- Timo Tonn, Karsten Urban, Stefan Volkwein, SIAM J. Scient. Comput. 32 no. 3, 1237-1260 (2010).
  52. A Mathematical Model for All Solid-State Lithium Ion Batteries- Katharina Becker-Steinberger, Stefan Funken, Manual Landstorfer, Karsten Urban, ECS Trans. 25 (36), 285 (2010).
  53. Simulation of Nasal Air Flow from MRI Data – a feasibility study- A. P. Wunderlich, B. Doll, M. Scheithauer, W. Freund, K. Urban, and U. Simon, Proc. of the 17th ISMRM Meeting (2009), p. 4668.
  54. A-posteriori Error Analysis of the Reduced Basis Method for Non-Affine Parameterized Nonlinear PDE's- Claudio Canuto, Timo Tonn, Karsten Urban, SIAM J. Numer. Anal. 47 3, 2001-2022 (2009)
  55. "Adaptive Wavelet Methods using Semiorthogonal Spline Wavelets:  Sparse Evaluation of Nonlinear Functions"- Kai Bittner, Karsten Urban, Appl. Comp. Harm. Anal. 24 (2008), 94-119.
  56. Simulation and Optimization in Fracture Healing- Daniel Nolte, Karsten Urban, Frank Niemeyer, Lutz Claes, Ulrich Simon, The Finite Element Method in Biomedical Engineering. Biomechanics and Related Fields, ISBN: 978-3-9806183-9-7, p. 34-43.
  57. "On Interpolatory Divergence-Free Wavelets"- Kai Bittner, Karsten Urban, Math. Comp. 76 (2007) 903-929.
  58. Numerical Optimization of the Voith-Schneider Propeller- Dirk Jürgens, Michael Palm, Sebastian Singer, Karsten Urban, ZAMM 87, No. 10 (2007), 698-710.
  59. "Adaptive Optimization in Convex Banach Spaces"- Claudio Canuto, Karsten Urban, SIAM J. Numer. Anal. 42 no. 5, (2004), 2043 - 2075. 
  60. "A convergent Wavelet-Rothe Method for Elastoplastic Hardening"- Giovanni Naldi, Karsten Urban, Paolo Venini, Arabian Journal for Science and Engineering, Theme Issue Wavelet and Fractal Methods in Science and Engineering, Part II, 29:2C (2004), 17-32.
  61. "On Fictitious Domain Formulations for Maxwell's Equations"- Wolfgang Dahmen, Torben Klint, Karsten Urban, Found. Comput. Math. 3 No. 2, 135-160 (2003) .
  62. "Adaptive Wavelet Methods -- Basic Concepts and Applications to the Stokes Problem"- Wolfgang Dahmen, Karsten Urban, Jürgen Vorloeper, In: Wavelet Analysis, D.-X. Zhou (ed.), World Scientific, New Jersey, 2002, 39-80. PDF-version of the preprint. 
  63. "Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates"- Stephan Dahlke, Wolfgang Dahmen, Karsten Urban, SIAM Journal on Numerical Analysis 40, No. 4 (2002)1230-1262.
  64. "Divergence-free wavelet analysis of turbulent flows"- Cem Albukrek, Karsten Urban, Dietmar Rempfer, John Lumley, Journal of Scientific Computing 17(1) (2002), 49-66.
  65. "Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments"- Arne Barinka, Titus Barsch, Philippe Charton, Albert Cohen, Stephan Dahlke, Wolfgang Dahmen, Karsten Urban, SIAM Journal of Scientific Computing 23, No. 3 (2001), 910-939.
  66. "A Wavelet-Galerkin Method for Elastoplasticity Problems"- Giovanni Naldi, Karsten Urban, Paolo Venini, Mathematical Modelling and Scientific Computing 10 (2000).
  67. "Adaptive Wavelet Methods for Saddle Point Problems"- Stephan Dahlke, Reinhard Hochmuth, Karsten Urban, M2AN 34, No. 5, 1003-1022 (2000).
  68. "Convergent Adaptive Wavelet Methods for the Stokes Problem"- Stephan Dahlke, Reinhard Hochmuth, Karsten Urban, In Multigrid Methods VI, E. Dick, K. Riemslagh, J. Vierendeels (eds.), Springer-Verlag, 2000, 66-72
  69. "Adaptive Wavelet Galerkin Methods on Distorted Domains: Setup of the Algebraic System"- Stefano Berrone, Karsten Urban, In Curve and Surface Fitting: Saint-Malo 1999, Albert Cohen, Christophe Rabut, and Larry L. Schumaker (eds.), Vanderbilt University Press, Nashville, TN, ISBN 0-8265-1357-3, 2000, 65-74.
  70. "Wavelet bases in H(div) and H(curl)"- Karsten Urban, Math. Comp. 70 (2001), 739-766.
  71. "On the adaptive computation of integrals of wavelets"- Silvia Bertoluzza, Claudio Canuto, Karsten Urban, Appl. Numer. Math. 34, 13-38 (2000).
  72. "Software Tools for using wavelets on the interval for the numerical solution of operator equations" - Titus Barsch, Karsten Urban, RWTH Aachen, IGPM report 158, 1998. In Concepts of Numerical Software, W. Hackbusch and G. Wittum (eds.), Univ. Kiel, 2000, 13-25.
  73. "Numerical Solution of Elliptic Problems by the Wavelet Element Method"- Claudio Canuto, Anita Tabacco, Karsten Urban, in: ENUMATH 97, H.G. Bock et al. (eds.), World Scientific, Singapore, 1998, 17-37.
  74. "The Wavelet Element Method, Part II: Realization and additional features in 2D and 3D"- Claudio Canuto, Anita Tabacco, Karsten Urban, Appl. Comp. Harm. Anal. 8, 123-165 (2000).
  75. "The Wavelet Element Method, Part I: Construction and Analysis"- Claudio Canuto, Anita Tabacco, Karsten Urban, Appl. Comp. Harm. Anal. 6, 1-52 (1999).
  76. "Wavelets in Numerical Analysis and their Quantitative Properties"- Wolfgang Dahmen, Angela Kunoth, Karsten Urban, In: Surface Fitting and Multiresolution Methods, A. Le Mehaute, C. Rabut, L.L. Schumaker (eds.), Vanderbilt University Press, Nashville, TN, 1997, 93-130.
  77. "Biorthogonal Spline-Wavelets on the Interval - Stability and Moment Conditions"- Wolfgang Dahmen, Angela Kunoth, Karsten Urban, Appl. Comp. Harm. Anal. 6, 132-196 (1999).
  78. "Towards Object Oriented Software Tools for Numerical Multiscale Methods for P.D.E.s using Wavelets"- Titus Barsch, Angela Kunoth, Karsten Urban, in: Multiscale Methods for Partial Differential Equations, W. Dahmen, A. Kurdilla, P. Oswald (eds.), Academic Press, 1997, 383-412.
  79. "A Wavelet-Galerkin Method applied to Separation Processes"- Rüdiger v. Watzdorf, Karsten Urban, Wolfgang Dahmen, Wolfgang Marquardt, in Scientific Computing in Cemical Engineering, S. Keil, W. Mackens, H. Voß, J. Werther (eds.), Springer-Verlag, Berlin, 1996, 246-252.
  80. "A Wavelet-Galerkin Method for the Stokes-Equations"- Wolfgang Dahmen, Angela Kunoth, Karsten Urban, Computing, 56, No. 3 (1996), 259-302. Abstract.
  81. "Using divergence free wavelets for the numerical solution of the Stokes problem"- Karsten Urban, in Algebraic Multilevel Iterations, O. Axelsson, B. Polman (ed.), Nijmegen, 1996, 259-278.
  82. "On Divergence-free Wavelets"- Karsten Urban, Advances in Computational Mathematics 4, No. 1,2, 51-82, 1995, Abstract.

 

Theses and Published Lecture Notes

  • "Multiskalenverfahren für das Stokes-Problem und angepaßte Wavelet-Basen" (PhD thesis, in german) - Karsten Urban, Verlag der Augustinus-Buchhandlung, Aachen, 1995. ISBN 3-86073-424-5. Zusammenfassung
  • "Beschränktheitsprinzipien in der Theorie der Rationalen Approximation" (in german) - Karsten Urban, Diplomarbeit (masters thesis), RWTH Aachen, 1992.

 

 

 

Software Documentations

  • "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 1.0, Documentation" - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper, RWTH Aachen, IGPM report 156, 1998.   
  • "The Multilevel Library: Software Tools for Multiscale Methods and Wavelets, Version 2.1, Documentation" - Arne Barinka, Titus Barsch, Karsten Urban, Jürgen Vorloeper, RWTH Aachen, IGPM report 205, 2001.

 

Other Articles and Manuscripts

  • Adaptive Wavelet Methods for Elliptic Variational Inequalitites I: Analysis - Mario Rometsch, Karsten Urban, University of Ulm, 2010.
  • A Reduced-Basis Method for Solving Parameter-Dependent Convection-Diffusion Problems Around Rigid Bodies - Timo Tonn, Karsten Urban, Proceedings of the ECCOMAS CFD 2006, no. 542, online (2006). "
  • Adaptive Wavelet Methods for the Numerical Solution of Operator Equations" - Karsten Urban, Oberwolfach report 10/2004, 522-525. 
  • "Quantitative Behaviour of Wavelet Bases" - Karsten Urban, Oberwolfach report 10/2004, 537-540. 
  • "Wavelet Based Methods in Elastoplasticity and Damage Analysis"- Giovanni Naldi, Paolo Venini, Karsten Urban, in Proceedings of ``Fifth World Congress on Computational Mechanics'', July 7-12, 2002, Vienna (Austria), H.A. Mang, F.G. Rammerstorfer, J. Eberhardsteiner (eds.), 2002.   
  • "On the Negative Invariance of Inertial Manifolds"- Gero Nießen, Karsten Urban, RWTH Aachen, IGPM report 141, 1997. Revised version Feb. 1998.    
  • "A Wavelet-Galerkin Algorithm for the Driven-Cavity-Stokes-Problem in two space dimensions",- Karsten Urban, in: Numerical Modelling in Continuum Mechanics, M. Feistauer, R. Rannacher, K. Kozel (eds.), Charles-University Prague, 278-289, 1995, Abstract.