Numerical methods for Friedrichs’ systems: Approximation theory, localized training and inherently stable model order reduction

Basic data of the doctoral examination procedure

Doctoral examination procedure finished at: Doctoral examination procedure at University of Münster

Period of time: 01/02/2021 - 10/01/2025

Status: completed

Candidate: Renelt, Lukas

Doctoral subject: Mathematik

Doctoral degree: Dr. rer. nat.

Form of the doctoral thesis: monographic

Awarded by: Department 10 - Mathematics and Computer Science

Supervisors: Ohlberger, Mario; Engwer, Christian

Reviewers: Ohlberger, Mario; Engwer, Christian; Vohralík; Martin

Promovend*in an der Universität Münster

Renelt, Lukas

Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Supervision at the University of Münster

Engwer, Christian	Professorship for Applications of Partial Differential Equations
Ohlberger, Mario	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Review at the University of Münster

Engwer, Christian	Professorship for Applications of Partial Differential Equations
Ohlberger, Mario	Professorship of Applied Mathematics, especially Numerics (Prof. Ohlberger)

Projects in which the doctoral examination procedure takes/took place

Cluster of Excellence 2044 - Mathematics Münster: Dynamics – Geometry – Structure (EXC 2044)

Duration: 01/01/2019 - 31/12/2025 | 1st Funding period

Funded by: DFG - Cluster of Excellence

Type of project: Main DFG-project hosted at University of Münster

Publications resulting from doctoral examination procedure

Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems Engwer, Christian; Ohlberger, Mario; Rebelt, Lukas (2025) In: arXiv:2507.00678. Research article in digital collection \| Preprint \| submitted / under review
Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems Kleikamp, Hendrik; Renelt, Lukas (2025) In: Journal of Scientific Computing, 104(78). doi:10.1007/s10915-025-02988-w Research article (journal) \| Published
Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems Engwer, Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: SIAM Journal on Scientific Computing, 46(5), A3205-A3229. doi:10.1137/23M1613402 Research article (journal) \| Peer reviewed \| Published
Construction of local reduced spaces for Friedrichs' systems via randomized training Engwer,Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: Central-European Conference on Scientific Computing, ALGORITMY, Podbanské, Slovakia. Proceedings of the Conference Algoritmy 2024. Research article in digital collection (conference) \| Peer reviewed \| Published
An optimally stable approximation of reactive transport using discrete test and infinite trial spaces Renelt, Lukas; Ohlberger, Mario; Engwer, Christian (2023) In: Franck, Emmanuel; Fuhrmann, Jürgen;, Michel-Dansac, Victor; Navoret, Laurent (eds.), Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, 289-298. Cham: Springer. doi:10.1007/978-3-031-40860-1_30 Research article in edited proceedings (conference) \| Peer reviewed \| Published

Sectional Kolmogorov N-widths for parameter-dependent function spaces: A general framework with application to parametrized Friedrichs' systems Engwer, Christian; Ohlberger, Mario; Rebelt, Lukas (2025) In: arXiv:2507.00678. Research article in digital collection \| Preprint \| submitted / under review
Two-stage model reduction approaches for the efficient and certified solution of parametrized optimal control problems Kleikamp, Hendrik; Renelt, Lukas (2025) In: Journal of Scientific Computing, 104(78). doi:10.1007/s10915-025-02988-w Research article (journal) \| Published
Model order reduction of an ultraweak and optimally stable variational formulation for parametrized reactive transport problems Engwer, Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: SIAM Journal on Scientific Computing, 46(5), A3205-A3229. doi:10.1137/23M1613402 Research article (journal) \| Peer reviewed \| Published
Construction of local reduced spaces for Friedrichs' systems via randomized training Engwer,Christian; Ohlberger, Mario; Renelt, Lukas (2024) In: Central-European Conference on Scientific Computing, ALGORITMY, Podbanské, Slovakia. Proceedings of the Conference Algoritmy 2024. Research article in digital collection (conference) \| Peer reviewed \| Published
An optimally stable approximation of reactive transport using discrete test and infinite trial spaces Renelt, Lukas; Ohlberger, Mario; Engwer, Christian (2023) In: Franck, Emmanuel; Fuhrmann, Jürgen;, Michel-Dansac, Victor; Navoret, Laurent (eds.), Finite Volumes for Complex Applications X—Volume 2, Hyperbolic and Related Problems, 289-298. Cham: Springer. doi:10.1007/978-3-031-40860-1_30 Research article in edited proceedings (conference) \| Peer reviewed \| Published