Universität Wien
Fakultät für Mathematik
Dr.techn. Marco Zank

Publikationen / Publications
L. Foltyn, D. Lukáš, M. Zank (2024): Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems. Accepted for publication in Comput. Methods Appl. Math., vol. 24, no. 2, 2024, pp. 431-443, DOI: 10.1515/cmam-2023-0085, Preprint. J. I. M. Hauser, M. Zank (2024): Numerical study of conforming space-time methods for Maxwell’s equations. Numer. Methods Partial Differ. Eq. 40, e23070, DOI: 10.1002/num.23070. M. Zank (2023): Integral Representations and Quadrature Schemes for the Modified Hilbert Transformation. Comput. Methods Appl. Math., vol. 23, no. 2, 2023, pp. 473-489, DOI: 10.1515/cmam-2022-0150. I. Perugia, Ch. Schwab, M. Zank (2023): Exponential convergence of hp-time-stepping in space-time discretizations of parabolic PDES. ESAIM Math. Model. Numer. Anal. 57.1, 29–67, DOI: 10.1051/m2an/2022081. M. Zank (2023): High-Order Discretisations and Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems. Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2020+1. Lecture Notes in Computational Science and Engineering, vol 137. Springer, Cham. DOI: 10.1007/978-3-031-20432-6_37. R. Löscher, O. Steinbach, M. Zank (2022): Numerical results for an unconditionally stable space-time finite element method for the wave equation. arXiv.org. Bericht 2021/3 aus dem Institut für Angewandte Mathematik, TU Graz. Domain Decomposition Methods in Science and Engineering XXVI. Vol. 145. Lect. Notes Comput. Sci. Eng. Springer, Cham, 625-632, DOI: 10.1007/978-3-030-95025-5_68. O. Steinbach, C. Urzúa-Torres, M. Zank (2022): Towards coercive boundary element methods for the wave equation. arXiv.org. Bericht 2021/10 aus dem Institut für Angewandte Mathematik, TU Graz. J. Integral Equations Appl. 34.4, 501–515, DOI: 10.1216/jie.2022.34.501. U. Langer, M. Zank (2021): Efficient Direct Space-Time Finite Element Solvers for Parabolic Initial-Boundary Value Problems in Anisotropic Sobolev Spaces. SIAM J. Sci. Comput., 43(4), A2714–A2736, DOI: 10.1137/20M1358128. O. Steinbach, M. Zank (2021): A generalized inf-sup stable variational formulation for the wave equation. J. Math. Anal. Appl. 505.1 (2022), Paper No. 125457, 24, DOI: 10.1016/j.jmaa.2021.125457. M. Zank (2021): Higher-Order Space-Time Continuous Galerkin Methods for the Wave Equation. arXiv.org. Proceeding in the 14th WCCM-ECCOMAS Congress 2020, DOI: 10.23967/wccm-eccomas.2020.167. M. Zank (2021): An Exact Realization of a Modified Hilbert Transformation for Space-Time Methods for Parabolic Evolution Equations. Comput. Methods Appl. Math. 21.2, 479–496, DOI: 10.1515/cmam-2020-0026. O. Steinbach, M. Zank (2021): A note on the efficient evaluation of a modified Hilbert transformation. Bericht 2019/8 aus dem Institut für Angewandte Mathematik, TU Graz. J. Numer. Math. 29.1, 47–61, DOI: 10.1515/jnma-2019-0099. M. Zank (2021): The Newmark Method and a Space–Time FEM for the Second–Order Wave Equation. Numerical mathematics and advanced applications. ENUMATH 2019. Vol. 139. Lect. Notes Comput. Sci. Eng. Springer, Cham, 1225–1233, DOI: 10.1007/978-3-030-55874-1_122. O. Steinbach, M. Zank (2020): Coercive space-time finite element methods for initial boundary value problems. Electron. Trans. Numer. Anal. 52, 154–194, DOI: 10.1553/etna_vol52s154. M. Zank (2020): Inf-Sup Stable Space-Time Methods for Time-Dependent Partial Differential Equations. Band 36 in Monographic Series TU Graz: Computation in Engineering and Science, Feber 2020, DOI: 10.3217/978-3-85125-721-2, Errata des Buchs. O. Steinbach, M. Zank (2019): A Stabilized Space–Time Finite Element Method for the Wave Equation. In: Apel T., Langer U., Meyer A., Steinbach O. (eds) Advanced Finite Element Methods with Applications. FEM 2017. Lecture Notes in Computational Science and Engineering, vol 128. Springer, Cham. M. Zank, O. Steinbach (2016): Adaptive space-time boundary element methods for the wave equation. Proc. Appl. Math. Mech., 16: 777-778, DOI: 10.1002/pamm.201610377.
Preprints
H. Harbrecht, Ch. Schwab, M. Zank (2024): Wavelet compressed, modified Hilbert transform in the space-time discretization of the heat equation. arXiv.org. R. Löscher, O. Steinbach, M. Zank (2024): On a modified Hilbert transformation, the discrete inf-sup condition, and error estimates. arXiv.org.
Abschlussarbeiten / Theses
M. Zank, Inf-Sup Stable Space-Time Methods for Time-Dependent Partial Differential Equations, Dissertation, TU Graz, Jänner 2019, Buch, Errata des Buchs. (Betreuer und Gutachter: Prof. Olaf Steinbach, TU Graz; Externer Gutachter: Prof. Christoph Schwab, ETH Zürich) M. Zank, Analysis und Numerik eines verallgemeinerten Steklov-Eigenwertproblems, Masterarbeit, TU Graz, 2014, Inhaltsverzeichnis. M. Zank, Numerische Betrachtung des Schrödinger-Steklov-Eigenwertproblems, Bak­ka­lau­re­ats­ar­beit (Projekt), TU Graz, 2013, Inhaltsverzeichnis. M. Zank, Analytische Betrachtung des Schrödinger-Steklov-Eigenwertproblems, Bak­ka­lau­re­ats­ar­beit (Seminar), TU Graz, 2013, Inhaltsverzeichnis.