Publications

Publication list (PDF): Link to PDF

Preprints

• A Priori and A Posteriori Error Identities for Vectorial Problems via Convex Duality
  ArXiv · February 2026 · arXiv
• Convection Effects and Optimal Insulation: Modelling and Analysis
  ArXiv · December 2025 · arXiv
• Pulsatile Flows for Simplified Smart Fluids with Variable Power-Law: Analysis and Numerics
  ArXiv · July 2025 · arXiv
• A Priori Error Analysis for the p-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
  ArXiv · July 2025 · arXiv
• Duality-based algorithm and numerical analysis for optimal insulation problems on non-smooth domains
  ArXiv · May 2025 · arXiv
• Error analysis for a fully-discrete finite element approximation of the unsteady p(⋅,⋅)-Stokes equations
  ArXiv · January 2025 · arXiv
• Conditional quasi-optimal error estimate for a finite element discretization of the p-Navier-Stokes equations: The case p>2
  ArXiv · October 2024 · arXiv
• Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
  ArXiv · August 2024 · arXiv

Peer-reviewed publications

• Blechta, J., Gazca-Orozco, P. A., Kaltenbach, A., Růžička, M. Quasi-optimal Discontinuous Galerkin discretisations of the $p$-Dirichlet problem. Numer. Math. (2026). https://doi.org/10.1007/s00211-025-01507-1 · DOI
• Kaltenbach, A., Zeinhofer, M. The Deep Ritz Method for parametric $p$-Dirichlet problems. Adv. Contin. Discrete Models 2026, Art. 8. https://doi.org/10.1186/s13662-025-04043-2 · DOI
• Antil, H., Bartels, S., Kaltenbach, A., Khandelwal, R. Variational problems with gradient constraints: A priori and a posteriori error identities. Math. Comp. (2025). https://doi.org/10.1090/mcom/4146 · DOI
• Antil, H., Kaltenbach, A., Kirk, K. L. A. Modeling and Analysis of an Optimal Insulation Problem on Nonsmooth Domains. SIAM J. Math. Anal. (2025). https://doi.org/10.1137/25M1741947 · DOI
• Berselli, L.C., Kaltenbach, A., Růžička, M. Energy conservation for weak solutions of incompressible Newtonian fluid equations in Hölder spaces with Dirichlet boundary conditions in the half-space. Math. Ann. (2024). https://doi.org/10.1007/s00208-024-03065-7 · DOI
• Bartels, S., Gudi, T., Kaltenbach, A. Error analysis for a Crouzeix–Raviart approximation of the variable exponent Dirichlet problem. IMA J. Numer. Anal. 63:5, 2155-2186 (2024). https://doi.org/10.1137/24M1677691 · DOI
• Balci, A., Kaltenbach, A. Error analysis for a Crouzeix–Raviart approximation of the variable exponent Dirichlet problem. IMA J. Numer. Anal. (2024). https://doi.org/10.1093/imanum/drae025 · DOI
• Gazca-Orozco, P. A., Kaltenbach, A. On the stability and convergence of discontinuous Galerkin schemes for incompressible flows. IMA J. Numer. Anal. (2024). https://doi.org/10.1093/imanum/drae004 · DOI
• Berselli, L. C., Kaltenbach, A. Convergence analysis of a fully-discrete finite element approximation of the unsteady $p(.,.)$-Navier-Stokes equations. Num. Math. (2025). https://doi.org/10.1007/s00211-025-01450-1 · DOI
• Kaltenbach, A., Růžička, M. Note on quasi-optimal error estimates for the pressure for shear-thickening fluids. ESAIM: Math. Model. Numer. Anal. (2024). https://doi.org/10.1016/bs.aams.2024.04.001 · DOI
• Berselli, L. C., Kaltenbach, A. Error analysis for a finite element approximation of the steady $p(.)$-Navier-Stokes equations. IMA J. Numer. Anal. 45, no. 5, 3026–3076. (2024). https://doi.org/10.1093/imanum/drae082 · DOI
• Jeßberger, J., Kaltenbach, A. Finite element discretization of the steady, generalized Navier–Stokes equations with inhomogeneous Dirichlet boundary conditions. SIAM J. Numer. Anal. 62:4, 1660-1686 (2024). https://doi.org/10.1137/23M1607398 · DOI
• Kaltenbach, A. Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem. J. Numer. Math. 32:2, 111–138 (2024). https://doi.org/10.1515/jnma-2022-0106 · DOI
• Kaltenbach, A., Růžička, M. A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part III: convergence rates for the pressure. SIAM J. Numer. Anal. 64:4, 1763-1782 (2023). https://doi.org/10.1137/22M1541472 · DOI
• Kaltenbach, A., Růžička, M. A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part II: convergence rates for the velocity. SIAM J. Numer. Anal. 64:4, 1641-1663 (2023). https://doi.org/10.1137/22M1514751 · DOI
• Kaltenbach, A., Růžička, M. A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part I: convergence analysis. SIAM J. Numer. Anal. 64:4, 1613–1640 (2023). https://doi.org/10.1137/22M151474X · DOI
• Bartels, S., Kaltenbach, A. Explicit a posteriori error representation for variational problems and application to TV-minimization. Found. Comput. Math. (2024). https://doi.org/10.1007/s10208-024-09676-5 · DOI
• Kaltenbach, A., Růžička, M. Existence of steady solutions for a general model for micropolar electrorheological fluid flows. SIAM J. Math. Anal. 55:3, 2238–2260 (2023). https://doi.org/10.1137/22M1500599 · DOI
• Kaltenbach, A., Růžička, M. Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications. Math. Models Methods Appl. Sci. 33:06, 1147-1192 (2023). https://doi.org/10.1142/S0218202523500197 · DOI
• Kaltenbach, A., Růžička, M. Convergence analysis of a Local Discontinuous Galerkin approximation for nonlinear systems with balanced Orlicz-structure. ESAIM: Math. Model. Numer. Anal. 57(3), 1381–1411 (2023). https://doi.org/10.1051/m2an/2023028 · DOI
• Kaltenbach, A., Růžička, M. Existence of steady solutions for a model for micropolar electrorheological fluid flows with not globally log-Hölder continuous shear exponent. J. Math. Fluid Mech. 25:40 (2023). https://doi.org/10.1007/s00021-023-00782-y · DOI
• Bartels, S., Kaltenbach, A. Explicit and efficient error estimation for convex minimization problems. Math. Comp. 92, 2247-2279 (2023). https://doi.org/10.1090/mcom/3821 · DOI
• Bartels, S., Kaltenbach, A. Error analysis for a Crouzeix-Raviart approximation of the obstacle problem. J. Numer. Math. (2025). https://doi.org/10.1515/jnma-2025-0036 · DOI
• Kaltenbach, A. Note on the existence theory for non-induced evolution equations. Mathematische Nachrichten. Math. Nachr. 295:6, 1186–1210 (2022). https://doi.org/10.1002/mana.201900555 · DOI
• Berselli, L. C., Kaltenbach, A., Lewandowski, R., Růžička, M. On the existence of weak solutions for a family of unsteady rotational Smagorinsky models. Pure Appl. Funct. Anal. 8:1, 83--102 (2023). http://yokohamapublishers.jp/online2/oppafa/vol8/p83.html · DOI
• Bartels, S., Kaltenbach, A. Error estimates for total-variation regularized minimization problems with singular dual solutions. Numer. Math. 152, 881–906 (2022). https://doi.org/10.1007/s00211-022-01324-w · DOI
• Berselli, L. C., Kaltenbach, A., Růžička, M. Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications. J. Math. Anal. Appl. 31:11, 2297-2343 (2021). https://doi.org/10.1142/S0218202521500494 · DOI
• Kaltenbach, A., Růžička, M. Variable exponent Bochner–Lebesgue spaces with symmetric gradient structure. J. Math. Anal. Appl. 503:2 (2021). https://doi.org/10.1016/j.jmaa.2021.125355 · DOI
• Kaltenbach, A., Růžička, M. Note on the existence theory for pseudo-monotone evolution problems. J. Evol. Equ. 21, 247–276 (2021). https://doi.org/10.1007/s00028-020-00577-y · DOI

Monographs

Book contributions

• Bartels, S., Kaltenbach, A. Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction. Adv. Appl. Mech. 58 (2024). https://doi.org/10.1016/bs.aams.2024.04.001
  DOI

Book publications

• Kaltenbach, A. Pseudo-monotone operator theory for unsteady problems with variable exponents. Lect. Notes Math. (2023). https://doi.org/10.1007/978-3-031-29670-3
  DOI

PhD thesis

• Kaltenbach, A. Theory of pseudo-monotone operators for unsteady problems in variable exponent spaces. Freidok University of Freiburg (2021). https://doi.org/10.6094/UNIFR/222538
  DOI