Prof. Dr. Patrick Henning

ArXiv Preprints

• C. Döding, P. Henning and J. Wärnegård.
  An efficient two level approach for simulating Bose-Einstein condensates.
  ArXiv e-print 2212.07392 (submitted), 2022.
• P. Henning and E. Jarlebring.
  The Gross-Pitaevskii equation and eigenvector nonlinearities: Numerical methods and algorithms.
   (submitted - available upon request), 2022.

2024

• 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 (to appear in SIAM J. Numer. Anal.), 2024.
• 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.

2023

• P. Henning.
  The dependency of spectral gaps on the convergence of the inverse iteration for a nonlinear eigenvector problem.
  M3AS Math. Models Methods Appl. Sci., 33(7):1517–1544, 2023. doi: 10.1142/S0218202523500343
  ArXiv e-print 2202.07593
• P. Henning and A. Persson.
  On optimal convergence rates for discrete minimizers of the Gross-Pitaevskii energy in LOD spaces.
  SIAM Multiscale Model. Simul., 21(3):993–1011, 2023. doi: 10.1137/22M1516300
  ArXiv e-print 2112.08485

2022

• P. Henning and J. Wärnegård.
  Superconvergence of time invariants for the Gross-Pitaevskii equation.
  Math. Comp., 91(334):509–555, 2022. doi: 10.1090/mcom/3693
  ArXiv e-print 2008.07575.
• R. Altmann, P. Henning and D. Peterseim.
  Localization and delocalization of ground states of Bose-Einstein condensates under disorder.
  SIAM J. Appl. Math., 82(1):330–358, 2022. doi: 10.1137/20M1342434.
  ArXiv e-print 2006.00773

2021

• R. Altmann, P. Henning and D. Peterseim.
  Numerical homogenization beyond scale separation.
  Acta Numer., 30:1–86, 2021. doi: https://doi.org/10.1017/S0962492921000015.
• R. Altmann, P. Henning and D. Peterseim.
  The J-method for the Gross-Pitaevskii eigenvalue problem.
  Numer. Math., 148(3):575–610, 2021. doi: 10.1007/s00211-021-01216-5.
  ArXiv e-print 1908.00333.
• P. Henning and A. M. N. Niklasson.
  Shadow Lagrangian dynamics for superfluidity.
  AIMS Kinetic & Related Models, 14(2):303–321, 2021. doi: 10.3934/krm.2021006
  ArXiv e-print 1912.10303
• P. Henning and J. Wärnegård.
  A note on optimal H1-error estimates for Crank-Nicolson approximations to the nonlinear Schrödinger equation.
  BIT Numer. Math., 61(1):37–59, 2021. doi: 10.1007/s10543-020-00814-3. 
  ArXiv e-print 1907.02782

2020

• P. Henning and D. Peterseim.
  Sobolev gradient flow for the Gross-Pitaevskii eigenvalue problem: global convergence and computational efficiency.
  SIAM J. Numer. Anal., 58(3):1744–1772, 2020. doi: 10.1137/18M1230463. 
  ArXiv e-print 1812.00835
• P. Henning and A. Persson.
  Computational homogenization of time-harmonic Maxwell's equations.
  SIAM J. Sci. Comput., 42(3):B581–B607, 2020. doi: 10.1137/19M1293818.
  ArXiv e-print 1910.07390
• R. Altmann, P. Henning and D. Peterseim.
  Quantitative Anderson localization of Schrödinger eigenstates under disorder potentials.
  M3AS Math. Models Methods Appl. Sci., 30(5):917–955, 2020. doi: 10.1142/S0218202520500190.
  ArXiv e-print 1803.09950

2019

• 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.

2018

• D. Gallistl, P. Henning and B. Verfürth.
  Numerical homogenization of H(curl)-problems.
  SIAM J. Numer. Anal., 56(3):1570–1596, 2018. doi: 10.1137/17M1133932
  ArXiv e-print 1706.02966.

2017

• 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.

2016

• 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.

2015

• 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. S, 8(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.

2014

• 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.

2013

• 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. 

2012

• 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.

2011

• P. Henning and M. Ohlberger.
  A note on homogenization of advection-diffusion problems with large expected drift.
  Z. Anal. Anwend., 30(3):319–339, 2011. doi: 10.4171/ZAA/1437.
  Preprint - Universität Münster.

2010

• 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.

2009

• 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.

Theses

• 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

• Mahima Yadav
• Maria Zimmermann

Former PhD students and postdocs          

• Dr. Christian Döding (now University Bonn)
• Dr. Benjamin Dörich (now Karlsruhe Institute of Technology)
• Dr. Anna Persson (now Uppsala University)    
• Dr. Johan  Wärnegård (now Columbia University)