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          • Julia Brunken
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Dr. Julia Brunken
© MFO
Dr. Julia Brunken
Scientific Assistant
Institute for Analysis and Numerics
Workgroup Prof. Ohlberger
julia.brunken@uni-muenster.de
 
  • Research Areas

    • Hierarchical Model Reduction
    • Transport Dominated Problems
    • Kinetic Equations
    • Reduced Basis Method
    • Space-Time Variational Formulations
  • Doctoral Thesis

    Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations

    Supervisors
    • Dr. Kathrin Smetana
    • Professor Dr. Mario Ohlberger

    We develop stable and efficient Petrov-Galerkin discretizations for two transport-dominated problems: first order linear transport equations and kinetic Fokker-Planck equations. Based on well-posed weak formulations we first choose a discrete test space for the Petrov-Galerkin projection. A problem-dependent discrete trial space is then computed such that the spaces consist of matching stable pairs of trial and test functions. Thereby we obtain efficiently computable and uniformly inf-sup stable discrete schemes. For parametrized transport equations, we apply the reduced basis method and build a reduced model consisting of a fixed reduced test space and parameter-dependent reduced trial spaces depending on the test space. Due to the inherent stability we can avoid additional stabilizations in the basis generation so that we obtain efficient reduced models by an easily implemented procedure.
    The whole thesis is available here.

  • Education

    10.​2013 - 07.​2015
    MSc. Mathematics with Minor in Physics
    10.​2010 - 09.​2013
    BSc. Mathematics with Minor in Physics
  • Teaching

    Winter Term 2020/21

    • Praktikum: Non-linear modelling in the natural sciences [102431]
      (in cooperation with Prof. Dr. Andreas Heuer, Prof. Dr. Christian Engwer, Priv.-Doz. Svetlana Gurevich, Tobias Leibner, Prof. Dr. Mario Ohlberger)

    Summer Term 2020

    • Übung: Tutorial Numerical Analysis of Partial Differential Equations II [100387]
      (in cooperation with Tobias Leibner, Prof. Dr. Mario Ohlberger)
    • Praktikum: Non-linear modelling in the natural sciences [100390]
      (in cooperation with Prof. Dr. Andreas Heuer, Prof. Dr. Christian Engwer, Priv.-Doz. Svetlana Gurevich, Tobias Leibner, Prof. Dr. Mario Ohlberger)

    Winter Term 2016/17

    • Übung: Tutorial Scientific Computing [106233]
      (in cooperation with Dr. Stephan Rave, Dr. Felix Schindler)

    Summer Term 2016

    • Übung: Tutorial Numerical Analysis of Partial Differential Equations II [104221]
      (in cooperation with Prof. Dr. Mario Ohlberger)
    • Praktikum: Introduction to Numerical Programming with Python [104225]
      (in cooperation with Dr. Felix Schindler, Prof. Dr. Mario Ohlberger)

    Winter Term 2015/16

    • Übung: Lab Course: Model Order Reduction for Partial Differential Equations [102162]
      (in cooperation with )

    Summer Term 2015

    • Praktikum: Introduction to Numerical Programming with Python [104875]
      (in cooperation with Prof. Dr. Mario Ohlberger)
  • Projects

    • GlioMaTh - Verbundprojekt 05M2016 - GlioMaTh: Gliomen, Mathematische Modelle und Therapieansätze - Teilprojekt 2 (2016 - 2019)
      Participation in BMBF-joint project: Federal Ministry of Education and Research | Project Number: 05M16PMA
  • Publications

    2021

    • Brunken Julia. 2021. Stable and efficient Petrov-Galerkin methods for certain (kinetic) transport equations Dissertation thesis, Universität Münster.

    2020

    • Brunken Julia Smetana Kathrin. 2020. ‘Stable and efficient Petrov-Galerkin methods for a kinetic Fokker-Planck equation.’ arXiv 2020. [submitted / under review]

    2019

    • Brunken Julia, Smetana Kathrin, Urban Karsten. 2019. ‘(Parametrized) First Order Transport Equations: Realization of Optimally Stable Petrov-Galerkin Methods.’ SIAM Journal on Scientific Computing 41, No. 1. doi: 10.1137/18M1176269.

    2016

    • Brunken Julia, Leibner Tobias, Ohlberger Mario, Smetana Kathrin. 2016. ‘Problem adapted hierachical model reduction for the Fokker-Planck equation.’ In ALGORITMY 2016 Proceedings of contributed papers and posters, edited by Handlovicova Angela, Sevcovic Daniel, 13–22. Bratislava: Slovak University of Technology in Bratislava.
  • Contacts
MathematicsMuensterCells in MotionSFB 656 MoBilDEMAIN – Developing Mathematics in InteractionCenter for Nonlinear ScienceCenter for Multiscale Theory and ComputationCompetence for Computing in Science

Contact

University of Münster
Angewandte Mathematik Münster

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48149 Münster

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