Prof. Dr. Patrick Henning

Chair of Numerical Mathematics

Ruhr-Uni­ver­si­ty Bo­chum
Fakulty of Mathematics
Uni­ver­si­täts­stra­ße 150
DE-44780 Bo­chum

Room: IB 3/133

Phone: +49 234 / 32-19611

Email: patrick.henning(at)

Research Interests

My research is concerned with the design and the analysis of numerical methods for solving multiscale differential equations. In particular, I am interested in

  • finite element methods
  • multiscale methods for partial differential equations
  • a priori and a posteriori error estimation
  • nonlinear Schrödinger equations
  • Maxwell's equations
  • computational quantum physics

Short CV

 2020 -Professor (Chair of Numerical Mathematics)
Department of Mathematics, Ruhr-University Bochum, Germany
 2018 - 2022Associate Professor
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
 05/2017Docent in Numerical Analysis
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
 2015 - 2018    Assistant Professor
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden
 2015Habilitation in Mathematics
University of Münster, Germany
 2014 - 2015Akademischer Rat (Assistant Lecturer)
Institute for Computational and Applied Mathematics, University of Münster, Germany
 2014Research Associate
Section de Mathématiques, École polytechnique fédérale de Lausanne, Switzerland
 2013 - 2014Research Associate
Division of Scientific Computing, Uppsala University, Sweden
 2011Doctorate in Mathematics (summa cum laude)
University of Münster, Germany
 2007 - 2013Research Associate
Institute for Computational and Applied Mathematics,
University of Münster, Germany
 2002 - 2007Diploma in Mathematics
University of Freiburg, Germany


ArXiv Preprints

  • P. Henning and M. Yadav.
    Convergence of a Riemannian gradient method for the Gross-Pitaevskii energy functional in a rotating frame.
    ArXiv e-print 2406.03885, 2024.
  • M. Blum, C. Döding and P. Henning.
    Vortex-capturing multiscale spaces for the Ginzburg-Landau equation.
    ArXiv e-print 2405.14772, 2024.
  • P. Henning and E. Jarlebring.
    The Gross-Pitaevskii equation and eigenvector nonlinearities: Numerical methods and algorithms.
     (submitted - available upon request), 2022.


  • C. Döding, P. Henning and J. Wärnegård.
    A two level approach for simulating Bose-Einstein condensates by localized orthogonal decomposition.
    ArXiv e-print 2212.07392 (to appear in M2AN Math. Model. Numer. Anal.), 2024.
  • B. Dörich and P. Henning.
    Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-κ regime.
    SIAM J. Numer. Anal., 62(3):1313–1343, 2024. doi: 10.1137/23M1560938.
    ArXiv e-print 2303.13961
  • P. Henning and M. Yadav.
    On discrete ground states of rotating Bose-Einstein condensates.
    ArXiv e-print 2303.00402 (to appear in Math. Comp.), 2024.
  • C. Döding and P. Henning.
    Uniform L∞-bounds for energy-conserving higher-order time integrators for the Gross-Pitaevskii equation with rotation.
    ArXiv e-print 2210.01553 (to appear in IMA Journal of Numerical Analysis), 2024.






  • P. Henning and J. Wärnegård.
    Numerical comparison of mass-conservative schemes for the Gross-Pitaevskii equation.
    AIMS Kinetic & Related Models, 12(6):1247–1271, 2019. doi: 10.3934/krm.2019048
    ArXiv e-print 1804.10547
  • C. Engwer, P. Henning, A. Målqvist, and D. Peterseim.
    Efficient implementation of the localized orthogonal decomposition method.
    Comput. Methods Appl. Mech. Engrg., 350:123–153, 2019. doi: 10.1016/j.cma.2019.02.040
    ArXiv e-print 1602.01658
  • P. Henning, R. Altmann, D. Peterseim, and J. Wärnegård.
    Numerical solution of nonlinear Schrödinger equations with highly variable potentials.
    In Computational Multiscale Methods, number 35 in Oberwolfach Reports, pages 21–24, august 2019. held 28 July - 3 August 2019. doi: 10.4171/OWR/2019/35.



  • A. Abdulle and P. Henning.
    Localized orthogonal decomposition method for the wave equation with a continuum of scales.
    Math. Comp., 86(304):549–587, 2017. doi: 10.1090/mcom/3114
    ArXiv e-print 1406.6325.
  • P. Henning and D. Peterseim.
    Crank-Nicolson Galerkin approximations to nonlinear Schrödinger equations with rough potentials.
    M3AS Math. Models Methods Appl. Sci., 27(11):2147–2184, 2017. doi: 10.1142/S0218202517500415
    ArXiv e-print 1608.02267.
  • A. Abdulle and P. Henning.
    Multiscale methods for wave problems in heterogeneous media.

    Handbook of Numerical Methods for Hyperbolic Problems: Applied and Modern Issues, Handbook of Numerical Analysis Vol. 18, Elsevier, Editors: Remi Abgrall, Chi-Wang Shu, 545–574, 2017. eBook ISBN: 9780444639110
    ArXiv e-print 1605.07922.
  • P. Henning and A. Målqvist.
    The Finite Element Method for the time-dependent Gross-Pitaevskii equation with angular momentum rotation.
    SIAM J. Numer. Anal., 55(2):923–952, 2017. doi: 10.1137/15M1009172
    ArXiv e-print 1502.05025.


  • P. Henning, M. Ohlberger, and B. Verfürth.
    A new heterogeneous multiscale method for time-harmonic Maxwell’s equations based on divergence-regularization.
    SIAM J. Numer. Anal., 54(6):3493–3522, 2016. doi: 10.1137/15M1039225
    ArXiv e-print 1509.03172.
  • P. Henning and A. Persson.
    A multiscale method for linear elasticity reducing poisson locking.
    Comput. Methods Appl. Mech. Engrg
    ., 310:156–171, 2016. doi: 10.1016/j.cma.2016.06.034
    ArXiv e-print 1603.09523.
  • P. Henning and M. Ohlberger.
    A-posteriori error estimate for a heterogeneous multiscale approximation of advection-diffusion problems with large expected drift.
    Discrete Contin. Dyn. Syst. Ser. S, 9(5):1393–1420, 2016. doi: 10.3934/dcdss.2016056.
  • F. Hellman, P. Henning, and A. Målqvist.
    Multiscale mixed finite elements.
    Discrete Contin. Dyn. Syst. Ser. S, 9(5):1269–1298, 2016. doi: 10.3934/dcdss.2016051
    ArXiv e-print 1501.05526.



  • P. Henning and A. Målqvist.
    Localized Orthogonal Decomposition Techniques for Boundary Value Problems.
    SIAM J. Sci. Comput., 36(4):A1609–A1634, 2014. doi: 10.1137/130933198.
    ArXiv e-print 1308.3379.
  • P. Henning, A. Målqvist, and D. Peterseim.
    A localized orthogonal decomposition method for semi-linear elliptic problems.
    M2AN Math. Model. Numer. Anal., 48:1331–1349, 2014. doi: 10.1051/m2an/2013141.
    ArXiv e-print 1211.3551.
  • P. Henning, A. Målqvist, and D. Peterseim.
    Two-Level Discretization Techniques for Ground State Computations of Bose-Einstein Condensates.
    SIAM J. Numer. Anal., 52(4):1525–1550, 2014. doi: 10.1137/130921520.
    ArXiv e-print 1305.4080.
  • P. Henning, M. Ohlberger, and B. Schweizer.
    An Adaptive Multiscale Finite Element Method.
    SIAM Multiscale Model. Simul., 12(3):1078–1107, 2014. doi: 10.1137/120886856.
  • P. Henning, A. Målqvist, and D. Peterseim.
    Two-level discretization for the Gross-Pitaevskii eigenvalue problem with a rough potential.
    In Computational Multiscale Methods, number 30 in Oberwolfach Reports, pages 29–32, july 2014. held 22 June - 28 June 2014. doi: 10.4171/OWR/2014/30.


  • P. Henning, M. Ohlberger, and B. Schweizer.
    Homogenization of the degenerate two-phase flow equations.
    M3AS Math. Models Methods Appl. Sci., 23(12):2323–2352, 2013. doi: 10.1142/S0218202513500334. 
  • P. Henning and D. Peterseim.
    Oversampling for the Multiscale Finite Element Method.
    SIAM Multiscale Model. Simul., 11(4):1149–1175, 2013. doi: 10.1137/120900332. 
    ArXiv e-print 1211.5954. 
  • M. Ohlberger, F. Albrecht, M. Drohmann, P. Henning, S. Kaulmann, and B. Schweizer.
    Model reduction for multiscale problems.
    In Multiscale and High-Dimensional Problems, number 39 in Oberwolfach Reports, pages 2228–2230, august 2013. held 28 July - 3 August 2013. doi: 10.4171/OWR/2013/39. 


  • P. Henning.
    Convergence of MSFEM approximations for elliptic, non-periodic homogenization problems.
    Netw. Heterog. Media, 7(3):503–524, 2012. doi: 10.3934/nhm.2012.7.503.
  • P. Henning and M. Ohlberger.
    A newton-scheme framework for multiscale methods for nonlinear elliptic homogenization problems.
    In Proceedings of the Algoritmy 2012, 19th Conference on Scientific Computing, Vysoke Tatry, Podbanske, September 9-14, 2012, pages 65–74, 2012. doi: 10.13140/2.1.4553.4727.
    Final PDF file 
  • P. Henning and M. Ohlberger.
    On the implementation of a heterogeneous multiscale finite element method for nonlinear elliptic problems.
    In R. Klöfkorn A. Dedner, B. Flemisch, editor, Advances in DUNE. Proceedings of the DUNE User Meeting, held 6.-8.10.2010, in Stuttgart, Germany., pages 143–155. Springer, 2012. doi: 10.1007/978-3-642-28589-9_11.
  • P. Bastian, H. Berninger, A. Dedner, C. Engwer, P. Henning, R. Kornhuber, D. Kröner, M. Ohlberger, O. Sander, G. Schiffler, N. Shokina, and K. Smetana.
    Adaptive modelling of coupled hydrological processes with application in water management.
    In Progress in Industrial Mathematics at ECMI 2010,, volume 17 of Mathematics in Industry,, pages 561–567. The European Consortium for Mathematics in Industry, Springer, 2012. doi: 10.1007/978-3-642-25100-9_65.



  • P. Henning and M. Ohlberger.
    The heterogeneous multiscale finite element method for advection-diffusion problems with rapidly oscillating coefficients and large expected drift.
    Netw. Heterog. Media, 5(4):711–744, 2010. doi: 10.3934/nhm.2010.5.711.


  • P. Henning and M. Ohlberger.
    The heterogeneous multiscale finite element method for elliptic homogenization problems in perforated domains.
    Numer. Math., 113(4):601–629, 2009. doi: 10.1007/s00211-009-0244-4.


  • P. Henning:
    Heterogeneous multiscale finite element methods for advection-diffusion and nonlinear elliptic multiscale problems. (PDF)
    PhD Thesis / Doktorarbeit, University of Münster, June 2011.  
  • P. Henning:
    Die heterogene Mehrskalenmethode für elliptische Differentialgleichungen in perforierten Gebieten. (PDF)
    Diploma Thesis, Mathematische Fakultät, University of Freiburg, May 2007. 


Current PhD students and postdocs
Former PhD students and postdocs          





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