On divergence-free wavelets. - Karsten Urban (Adv. Comput. Math., 1995)

A Wavelet Galerkin Method for the Stokes Equations. - Wolfgang Dahmen; Angela Kunoth; Karsten Urban (Computing, 1996)

Wavelet bases in H(div) and H(curl). - Karsten Urban (Math. Comput., 2001)

Adaptive Wavelet Schemes for Elliptic Problems - Implementation and Numerical Experiments. - Arne Barinka; Titus Barsch; Philippe Charton; Albert Cohen 002; Stephan Dahlke; Wolfgang Dahmen; Karsten Urban (SIAM J. Sci. Comput., 2001)

Divergence-Free Wavelet Analysis of Turbulent Flows. - Cem M. Albukrek; Karsten Urban; Dietmar Rempfer; John L. Lumley (J. Sci. Comput., 2002)

Adaptive Wavelet Methods for Saddle Point Problems - Optimal Convergence Rates. - Stephan Dahlke; Wolfgang Dahmen; Karsten Urban (SIAM J. Numer. Anal., 2002)

Wavelets in Numerical Simulation - Problem Adapted Construction and Applications. - Karsten Urban (Springer, 2002)

On Fictitious Domain Formulations for Maxwell's Equations. - Wolfgang Dahmen; Torben Klint; Karsten Urban (Found. Comput. Math., 2003)

Adaptive Optimization of Convex Functionals in Banach Spaces. - Claudio Canuto; Karsten Urban (SIAM J. Numer. Anal., 2005)

On interpolatory divergence-free wavelets. - Kai Bittner; Karsten Urban (Math. Comput., 2007)

A Posteriori Error Analysis of the Reduced Basis Method for Nonaffine Parametrized Nonlinear PDEs. - Claudio Canuto; Timo Tonn; Karsten Urban (SIAM J. Numer. Anal., 2009)

Optimal Control of Parameter-Dependent Convection-Diffusion Problems around Rigid Bodies. - Timo Tonn; Karsten Urban; Stefan Volkwein (SIAM J. Sci. Comput., 2010)

Automatic differentiation for the optimization of a ship propulsion and steering system: a proof of concept. - Ralf Leidenberger; Karsten Urban (J. Glob. Optim., 2011)

Adaptive Wavelet Methods on Unbounded Domains. - Sebastian Kestler; Karsten Urban (J. Sci. Comput., 2012)

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. Uncertain. Quantification, 2013)

An improved error bound for reduced basis approximation of linear parabolic problems. - Karsten Urban; Anthony T. Patera (Math. Comput., 2014)

Comparison of the EM algorithm and alternatives. - Theresa Springer; Karsten Urban (Numer. Algorithms, 2014)

On Noncoercive Variational Inequalities. - Silke Glas; Karsten Urban (SIAM J. Numer. Anal., 2014)

Reduced Basis Exact Error Estimates with Wavelets. - Mazen Ali; Karsten Urban (ENUMATH, 2015)

Model order reduction of parameterized systems (MoRePaS) - Preface to the special issue of advances in computational mathematics. - Peter Benner; Mario Ohlberger; Anthony T. Patera; Gianluigi Rozza; Danny C. Sorensen; Karsten Urban (Adv. Comput. Math., 2015)

Adjoint-Based Optimization for Rigid Body Motion in Multiphase Navier-Stokes Flow. - Julia Springer; Karsten Urban (SIAM J. Sci. Comput., 2015)

An efficient space-time adaptive wavelet Galerkin method for time-periodic parabolic partial differential equations. - Sebastian Kestler; Kristina Steih; Karsten Urban (Math. Comput., 2016)

Reduced basis methods with adaptive snapshot computations. - Mazen Ali; Kristina Steih; Karsten Urban (Adv. Comput. Math., 2017)

A Variational Formulation for LTI-Systems and Model Reduction. - Moritz Feuerle; Karsten Urban (ENUMATH, 2019)

Matrix Oriented Reduction of Space-Time Petrov-Galerkin Variational Problems. - Julian Henning; Davide Palitta; Valeria Simoncini; Karsten Urban (ENUMATH, 2019)

A hierarchical a posteriori error estimator for the Reduced Basis Method. - Stefan Hain; Mario Ohlberger; Mladjan Radic; Karsten Urban (Adv. Comput. Math., 2019)

Decay of the Kolmogorov N-width for wave problems. - Constantin Greif; Karsten Urban (Appl. Math. Lett., 2019)

(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods. - Julia Brunken; Kathrin Smetana; Karsten Urban (SIAM J. Sci. Comput., 2019)

HT-AWGM: a hierarchical Tucker-adaptive wavelet Galerkin method for high-dimensional elliptic problems. - Mazen Ali; Karsten Urban (Adv. Comput. Math., 2020)

A Space-Time Variational Method for Optimal Control Problems. - Nina Beranek; M. Alexander Reinhold; Karsten Urban (CoRR, 2020)

Very Weak Space-Time Variational Formulation for the Wave Equation: Analysis and Efficient Numerical Solution. - Julian Henning; Davide Palitta; Valeria Simoncini; Karsten Urban (CoRR, 2021)

Linear/Ridge expansions: enhancing linear approximations by ridge functions. - Constantin Greif; Philipp Junk; Karsten Urban (Adv. Comput. Math., 2022)

A certified wavelet-based physics-informed neural network for the solution of parameterized partial differential equations. - Lewin Ernst; Karsten Urban (CoRR, 2022)

An Ultraweak Variational Method for Parameterized Linear Differential-Algebraic Equations. - Emil Beurer; Moritz Feuerle; Niklas Reich; Karsten Urban (Frontiers Appl. Math. Stat., 2022)

A space-time variational method for optimal control problems: well-posedness, stability and numerical solution. - Nina Beranek; Martin Alexander Reinhold; Karsten Urban (Comput. Optim. Appl., 2023)

A parallel batch greedy algorithm in reduced basis methods: Convergence rates and numerical results. - Niklas Reich; Karsten Urban; Jürgen Vorloeper (CoRR, 2024)

An ultra-weak space-time variational formulation for the Schrödinger equation. - Stefan Hain; Karsten Urban (J. Complex., 2024)

A posteriori certification for physics-informed neural networks. - Lewin Ernst; Nikolaos Rekatsinas; Karsten Urban (CoRR, 2025)

The Kolmogorov N-width for linear transport: exact representation and the influence of the data. - Florian Arbes; Constantin Greif; Karsten Urban (Adv. Comput. Math., 2025)

A unified framework for the analysis, numerical approximation and model reduction of linear operator equations, Part I: Well-posedness in space and time. - Moritz Feuerle; Richard Löscher; Olaf Steinbach; Karsten Urban (CoRR, 2025)