Faculty of Mathematics » Chair: Numerical Analysis

Faculty of Mathematics
Universitätsstraße 150
DE-44801 Bochum

Office: IB 3-133

Tel.: +49 234 / 32 - 19 611

Email: patrick.henning@rub.de

Office hours: upon request by email


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

Team members

Past members

Short CV

 2020 - Professor (Chair of Numerical Mathematics)
Department of Mathematics, Ruhr-University Bochum, Germany

 2018 - Associate Professor
Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden

 05/2017 Docent 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

 2015 Habilitation in Mathematics
University of Münster, Germany

 2014 - 2015 Akademischer Rat (Assistant Lecturer)
Institute for Computational and Applied Mathematics, University of Münster, Germany

 2014 Research Associate
Section de Mathématiques, École polytechnique fédérale de Lausanne, Switzerland

 2013 - 2014 Research Associate
Division of Scientific Computing, Uppsala University, Sweden

 2011 Doctorate in Mathematics (summa cum laude)
University of Münster, Germany

 2007 - 2013 Research Associate
Institute for Computational and Applied Mathematics,
University of Münster, Germany

 2002 - 2007 Diploma in Mathematics
University of Freiburg, Germany


List of publications

ArXiv Preprints

  • B. Dörich and P. Henning.
    Error bounds for discrete minimizers of the Ginzburg-Landau energy in the high-κ regime.
    ArXiv e-print 2303.13961 (submitted), 2023.

  • P. Henning and M. Yadav.
    On discrete ground states of rotating Bose-Einstein condensates.
    ArXiv e-print 2303.00402 (submitted), 2023.

  • C. Döding, P. Henning and J. Wärnegård.
    An efficient two level approach for simulating Bose-Einstein condensates.
    ArXiv e-print 2212.07392 (submitted), 2022.

  • 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 (submitted), 2022.

  • P. Henning and E. Jarlebring.
    The Gross-Pitaevskii equation and eigenvector nonlinearities: Numerical methods and algorithms.
     (submitted - available upon request), 2022.


  • P. Henning.
    The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem.
    ArXiv e-print 2202.07593 (to appear in M3AS), 2023.

  • P. Henning and A. Persson.
    On optimal convergence rates for discrete minimizers of the Gross-Pitaevskii energy in LOD spaces.
    ArXiv e-print 2112.08485 (to appear in SIAM MMS), 2023.





  • 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.


  • A. Abdulle and P. Henning.
    A reduced basis localized orthogonal decomposition.
    J. Comput. Phys., 295:379–401, 2015. doi: 10.1016/j.jcp.2015.04.016.
    ArXiv e-print 1410.3253.

  • D. Elfverson, V. Ginting, and P. Henning.
    On multiscale methods in Petrov-Galerkin formulation.
    Numer. Math., 131(4):643–682, 2015. doi: 10.1007/s00211-015-0703-z.
    ArXiv e-print 1405.5758.

  • P. Henning and M. Ohlberger.
    Error control and adaptivity for heterogeneous multiscale approximations of nonlinear monotone problems.
    Discrete Contin. Dyn. Syst. Ser. S8(1):119–150, 2015. doi: 10.3934/dcdss.2015.8.119.

  • P. Henning, M. Ohlberger, and B. Schweizer.
    Adaptive Heterogeneous Multiscale Methods for immiscible two-phase flow in porous media.
    Comput. Geosci., 19(1):99–114, 2015. doi: 10.1007/s10596-014-9455-6.
    ArXiv e-print 1307.2123.

  • P. Henning, P. Morgenstern, and D. Peterseim.
    Multiscale partition of unity.
    In Michael Griebel and Marc Alexander Schweitzer, editors, Meshfree Methods for Partial Differential Equations VII, volume 100 of Lecture Notes in Computational Science and Engineering, pages 185–204. Springer International Publishing, 2015. doi: 10.1007/978-3-319-06898-5_10.
    ArXiv e-print 1312.5922.


  • 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.
    Preprint - Universität Münster

  • 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.