Address

RWTH Aachen University
Institut für Geometrie und Praktische Mathematik 114620
Im Süsterfeld 2, room 403
52072 Aachen

Phone

+49 241 80 93069

Email

kolbe AT igpm DOT rwth-aachen DOT de

Web

nklb.gitlab.io/

Research Area

Numerical methods, scientific computing, partial differential equations, mathematical modeling, cancer biology, stochastic models

Publications

• Central schemes for networked scalar conservation laws
  M. Herty, N. Kolbe, and S. Müller
  Netw. Heterog. Media 18 (2023), no.1, 310–340
  doi: 10.3934/nhm.2023012
  Preprint arXiv:2209.05137

• Numerical relaxation limit and outgoing edges in a central scheme for networked conservation laws
  N. Kolbe
  doi: 10.1002/pamm.202200150
  Preprint arXiv:2210.03573

• Data-Driven Models for Traffic Flow at Junctions
  M. Herty and N. Kolbe
  Math. Methods Appl. Sci. 47 (2024), no. 11, 8946–8968
  doi: 10.1002/mma.10053
  Preprint arXiv:2212.08912

• A central scheme for two coupled hyperbolic systems
  M. Herty, N. Kolbe, and S. Müller
  doi: 10.1007/s42967-023-00306-5
  Preprint arXiv:2304.13946

• A data-driven microscopic on-ramp model based on macroscopic network flows
  N. Kolbe, M. Berghaus, E. Kalló, M. Herty, and M. Oeser
  Preprint arXiv:2308.01093

• A posteriori error analysis of a positivity preserving scheme for the power-law diffusion Keller-Segel model
  J. Giesselmann and N. Kolbe
  IMA Journal of Numerical Analysis (2025) 45, 2791–2823
  doi: 10.1093/imanum/drae073
  Preprint arXiv:2309.07329

• Numerical schemes for coupled systems of nonconservative hyperbolic equations
  N. Kolbe, M. Herty, and S. Müller
  SIAM journal on numerical analysis 62 (5) (2024), pp.2143-2171
  doi: 10.1137/23M1615176
  Preprint arXiv:2311.03581

• Error Estimates for First- and Second-Order Lagrange–Galerkin Moving Mesh Schemes for the One-Dimensional Convection–Diffusion Equation
  K.S. Putri, T. Mizuochi, N. Kolbe, and H. Notsu
  J Sci Comput 101, 37 (2024)
  doi: 10.1007/s10915-024-02673-4
  Preprint arXiv:2402.14691

• A one-dimensional model for aspiration in blood vessels
  N. Kolbe, D. Katsaounis, X. Yin, and M. Neidlin
  Preprint arXiv:2403.05494

• Influx ratio preserving coupling conditions for the networked Lighthill–Whitham–Richards model
  N. Kolbe
  Proceedings in Applied Mathematics and MechanicsVolume 24, Issue 4: Special Issue: 94th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) Dec 2024
  doi: 10.1002/pamm.202400197
  Preprint arXiv:2405.21005

• A Microscopic On-Ramp Model Based on Macroscopic Network Flows
  N. Kolbe, J.M. Berghaus, E. Kalló, M. Herty, and M. Oeser
  Appl. Sci. 2024, 14, 9111
  doi: 10.3390/app14199111

• A relaxation approach to the coupling of a two-phase fluid with a linear-elastic solid
  N. Kolbe and S. Müller
  Applied mathematics and computation 504, Issue C (2025)
  doi: 10.1016/j.amc.2025.129503
  Preprint arXiv:2409.05473

• The Lax-Friedrichs method in one-dimensional hemodynamics
  A. Beckers and N. Kolbe
  Preprint arXiv:2501.16115

• The Lax–Friedrichs method in one-dimensional hemodynamics and its simplifying effect on boundary and coupling conditions
  A. Beckers and N. Kolbe
  Computer Methods in Biomechanics and Biomedical Engineering (2025), 1–14
  doi: 10.1080/10255842.2025.2532027

• Discontinuous Galerkin schemes for multi-dimensional coupled hyperbolic systems
  N. Kolbe, S. Müller, and A. Sikstel
  Preprint arXiv:2601.11172