Publications

D. Kuzmin, H. Hajduk (2023) Property-preserving numerical schemes for conservation laws (World Scientific), doi:10.1142/13466

D. Kuzmin, H. Hajduk, J. Vedral (2026) An element-based convex limiting framework for continuous Galerkin methods with nonlinear stabilization. J. Comput. Phys. 560: 114952, doi:10.1016/j.jcp.2026.114952

J. H. Lacasce, H. Hajduk, J. Brændshøi (2026) Unstable Rossby waves over bathymetry. J. Fluid Mech. 1034: A10, doi:10.1017/jfm.2026.11482

H. Hajduk (2025) Improvements of algebraic flux-correction schemes based on Bernstein finite elements. J. Numer. Math. 33: 375-402, doi:10.1515/jnma-2024-0098

H. Hajduk, D. Kuzmin, G. Lube, P. Öffner (2025) Locally energy-stable finite element schemes for incompressible flow problems: Design and analysis for equal-order interpolations. Comput. Fluids 294: 106622, doi:10.1016/j.compfluid.2025.106622

H. Hajduk, A. Rupp (2023) Analysis of algebraic flux correction for semi-discrete advection problems. BIT Numer. Math. 63: 8, doi:10.1007/s10543-023-00957-z

D. Kuzmin, H. Hajduk, A. Rupp (2022) Limiter-based entropy stabilization of semi-discrete and fully discrete schemes for nonlinear hyperbolic problems. Comput. Methods Appl. Mech. Eng. 389: 114428, doi:10.1016/j.cma.2021.114428

H. Hajduk (2021) Monolithic convex limiting in discontinuous Galerkin discretizations of hyperbolic conservation laws. Comput. Math. Appl. 87: 120-138, doi:10.1016/j.camwa.2021.02.012

B. Reuter, H. Hajduk, A. Rupp, F. Frank, V. Aizinger, P. Knabner (2021) FESTUNG 1.0: Overview, usage, and example applications of the MATLAB / GNU Octave toolbox for discontinuous Galerkin methods. Comput. Math. Appl. 81: 3-41, doi:10.1016/j.camwa.2020.08.018

M. Hauck, V. Aizinger, F. Frank, H. Hajduk, A. Rupp (2020) Enriched Galerkin method for the shallow-water equations. Int. J. Geomath. 11: 31, doi:10.1007/s13137-020-00167-7

D. Kuzmin, H. Hajduk, A. Rupp (2020) Locally bound-preserving enriched Galerkin methods for the linear advection equation. Comput. Fluids 205: 104525, doi:10.1016/j.compfluid.2020.104525

M. Wang, Z. Wang, H. Hajduk (2020) Nonlinear interactions of nearly non-dispersive equatorial shallow-water waves. IMA J. Appl. Math. 85: 365-384, doi:10.1093/imamat/hxaa009

H. Hajduk, D. Kuzmin, T. Kolev, V. Tomov, I. Tomas, J. N. Shadid (2020) Matrix-free subcell residual distribution for Bernstein finite elements: Monolithic limiting. Comput. Fluids 200: 104451, doi:10.1016/j.compfluid.2020.104451

H. Hajduk, D. Kuzmin, T. Kolev, R. Abgrall (2020) Matrix-free subcell residual distribution for Bernstein finite element discretizations of linear advection equations. Comput. Methods Appl. Mech. Eng. 359: 112658, doi:10.1016/j.cma.2019.112658

H. Hajduk, D. Kuzmin, V. Aizinger (2019) New directional vector limiters for discontinuous Galerkin methods. J. Comput. Phys. 384: 308-325, doi:10.1016/j.jcp.2019.01.032

H. Hajduk, B. R. Hodges, V. Aizinger, B. Reuter (2018) Locally filtered transport for computational efficiency in multi-component advection-reaction models. Environ. Modell. Softw. 102: 185-198, doi:10.1016/j.envsoft.2018.01.003

H. Hajduk, D. Kuzmin (2022) Bound-preserving and entropy-stable algebraic flux correction schemes for the shallow water equations with topography. In Eleventh international conference on computational fluid dynamics (ICCFD11 proceedings), URL: https://www.iccfd.org/iccfd11/assets/pdf/papers/ICCFD11_Paper-3003.pdf

H. Hajduk, D. Kuzmin, V. Aizinger (2020) Bathymetry reconstruction using inverse shallow water models: Finite element discretization and regularization. In Numerical methods for flows, Lecture notes in computational science and engineering, 223-230 (Springer), doi:10.1007/978-3-030-30705-9_20

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H. Hajduk (2022) Algebraically constrained finite element methods for hyperbolic problems with applications in geophysics and gas dynamics. Ph.D. thesis, TU Dortmund University, doi:10.17877/DE290R-22850

H. Hajduk (2017) Numerical investigation of direct bathymetry reconstruction based on a modified shallow-water model. Master's thesis, Friedrich-Alexander-University Erlangen-Nuremberg

H. Hajduk (2014) Optimal estimates on the waiting time for the porous media equation. (translated title) Bachelor's thesis, Friedrich-Alexander-University Erlangen-Nuremberg