Mathematical modelling for an optimal insulation problem on Lipschitz domains
Published in ArXiv, 2025
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Publications
Publication list (in PDF format): Link to PDF
Preprints
Error analysis for a fully-discrete finite element approximation of the unsteady p(⋅,⋅)-Stokes equations
Published in ArXiv, 2025
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Conditional quasi-optimal error estimate for a finite element discretization of the p-Navier-Stokes equations: The case p>2
Published in ArXiv, 2024
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Variational problems with gradient constraints: A priori and a posteriori error identities
Published in ArXiv, 2024
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Finite element discretization of the steady, generalized Navier-Stokes equations for small shear stress exponents
Published in ArXiv, 2024
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A priori and a posteriori error identities for the scalar Signorini problem
Published in ArXiv, 2024
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Convergence analysis of a fully-discrete finite element approximation of the unsteady $p(.,.)$-Navier-Stokes equations
Published in ArXiv, 2024
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Quasi-optimal Discontinuous Galerkin discretisations of the p-Dirichlet problem
Published in ArXiv, 2023
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Error analysis for a Crouzeix-Raviart approximation of the obstacle problem
Published in ArXiv, 2023
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The Deep Ritz Method for Parametric p-Dirichlet Problems
Published in ArXiv, 2022
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Peer-reviewed Publications
Energy conservation for weak solutions of incompressible Newtonian fluid equations in Hölder spaces with Dirichlet boundary conditions in the half-space
Published in Mathematische Annalen, 2024
Recommended citation: Berselli, L.C., Kaltenbach, A., and 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 https://doi.org/10.1007/s00208-024-03065-7
Error analysis for a Crouzeix–Raviart approximation of the variable exponent Dirichlet problem
Published in IMA Journal of Numerical Analysis, 2024
Recommended citation: 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 https://doi.org/10.1093/imanum/drae025
On the stability and convergence of discontinuous Galerkin schemes for incompressible flows
Published in IMA Journal of Numerical Analysis, 2024
Recommended citation: 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 https://doi.org/10.1093/imanum/drae004
Note on quasi-optimal error estimates for the pressure for shear-thickening fluids
Published in ESAIM: Mathematical Modelling and Numerical Analysis, 2024
Recommended citation: 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 https://doi.org/10.1051/m2an/2024051
Error analysis for a finite element approximation of the steady $p(.)$-Navier-Stokes equations
Published in IMA Journal of Numerical Analysis, 2023
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Finite element discretization of the steady, generalized Navier-Stokes equations with inhomogeneous Dirichlet boundary conditions
Published in SIAM Journal on Numerical Analysis, 2023
Recommended citation: 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 https://epubs.siam.org/doi/abs/10.1137/23M1607398
Error analysis for a Crouzeix–Raviart approximation of the p-Dirichlet problem
Published in Journal of Numerical Mathematics, 2023
Recommended citation: 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 https://doi.org/10.1515/jnma-2022-0106
A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part III: convergence rates for the pressure
Published in SIAM Journal on Numerical Analysis, 2023
Recommended citation: 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 https://doi.org/10.1137/22M1541472
A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part II: convergence rates for the velocity
Published in SIAM Journal on Numerical Analysis, 2023
Recommended citation: 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 https://doi.org/10.1137/22M1514751
A Local Discontinuous Galerkin approximation for the p-Navier–Stokes system, part I: convergence analysis
Published in SIAM Journal on Numerical Analysis, 2023
Recommended citation: 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 https://doi.org/10.1137/22M151474X
Explicit a posteriori error representation for variational problems and application to TV-minimization
Published in Journal of Foundations of Computational Mathematics, 2023
Recommended citation: 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 https://doi.org/10.1007/s10208-024-09676-5
Existence of steady solutions for a general model for micropolar electrorheological fluid flows
Published in SIAM Journal on Mathematical Analysis, 2023
Recommended citation: 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 https://doi.org/10.1137/22M1500599
Analysis of a fully-discrete, non-conforming approximation of evolution equations and applications
Published in Mathematical Models and Methods in Applied Sciences, 2023
Recommended citation: 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 https://doi.org/10.1142/S0218202523500197
Convergence analysis of a Local Discontinuous Galerkin approximation for nonlinear systems with balanced Orlicz-structure
Published in ESAIM: Mathematical Modelling and Numerical Analysis (ESAIM: M2AN), 2023
Recommended citation: 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 https://doi.org/10.1051/m2an/2023028
Existence of steady solutions for a model for micropolar electrorheological fluid flows with not globally log-Hölder continuous shear exponent
Published in Journal of Mathematical Fluid Mechanics, 2023
Recommended citation: 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 https://doi.org/10.1007/s00021-023-00782-y
Explicit and efficient error estimation for convex minimization problems
Published in Mathematics of Computation, 2023
Recommended citation: 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 https://doi.org/10.1090/mcom/3821
Note on the existence theory for non-induced evolution equations
Published in Mathematische Nachrichten, 2022
Recommended citation: 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 https://doi.org/10.1002/mana.201900555
On the existence of weak solutions for a family of unsteady rotational Smagorinsky models
Published in Pure and Applied Functional Analysis, 2022
Recommended citation: 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 http://yokohamapublishers.jp/online2/oppafa/vol8/p83.html
Error estimates for total-variation regularized minimization problems with singular dual solutions
Published in Numerische Mathematik, 2021
Recommended citation: 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 https://doi.org/10.1007/s00211-022-01324-w
Analysis of fully discrete, quasi non-conforming approximations of evolution equations and applications
Published in Mathematical Models and Methods in Applied Sciences, 2021
Recommended citation: 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 https://doi.org/10.1142/S0218202521500494
Variable exponent Bochner–Lebesgue spaces with symmetric gradient structure
Published in Journal of Mathematical Analysis and Applications, 2021
Recommended citation: 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 https://doi.org/10.1016/j.jmaa.2021.125355
Note on the existence theory for pseudo-monotone evolution problems
Published in Journal of Evolution Equations, 2020
Recommended citation: 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 https://doi.org/10.1007/s00028-020-00577-y
Monographs
Book Contributions
Exact a posteriori error control for variational problems via convex duality and explicit flux reconstruction
Published in Advances in Applied Mechanics, 2024
Recommended citation: 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 https://doi.org/10.1016/bs.aams.2024.04.001
Book Publications
Pseudo-monotone operator theory for unsteady problems with variable exponents
Published in Lecture Notes in Mathematics, 2023
Recommended citation: 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 https://doi.org/10.1007/978-3-031-29670-3
PhD Thesis
Theory of pseudo-monotone operators for unsteady problems in variable exponent spaces
Published in Lecture Notes in Mathematics, 2021
Recommended citation: 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 https://doi.org/10.6094/UNIFR/222538