Publications

In journals

• L. Gauckler, On energy conservation by trigonometric integrators in the linear case with application to wave equations, J. Comput. Math. 38 (2020), 705-714.
  [ paper | preprint ]
• L. Gauckler, J. Lu, J. L. Marzuola, F. Rousset, K. Schratz, Trigonometric integrators for quasilinear wave equations, Math. Comp. 88 (2019), 717-749.
  [ paper | preprint ]
• L. Gauckler, On a splitting method for the Zakharov system, Numer. Math. 139 (2018), 349-379.
  [ paper | preprint ]
• S. Buchholz, L. Gauckler, V. Grimm, M. Hochbruck, T. Jahnke, Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations, IMA J. Numer. Anal. 38 (2018), 57-74.
  [ paper | preprint ]
• L. Gauckler, Numerical long-time energy conservation for the nonlinear Schrödinger equation, IMA J. Numer. Anal. 37 (2017), 2067-2090.
  [ paper | free access link ]
• L. Gauckler, H. Yserentant, Structure preserving discretization of the chemical master equation, BIT 57 (2017), 753-770.
  [ paper ]
• L. Gauckler, D. Weiss, Metastable energy strata in numerical discretizations of weakly nonlinear wave equations, Discrete Contin. Dyn. Syst. 37 (2017), 3721-3747.
  [ paper | preprint ]
• L. Gauckler, E. Hairer, C. Lubich, Long-term analysis of semilinear wave equations with slowly varying wave speed, Comm. Partial Differential Equations 41 (2016), 1934-1959.
  [ paper | preprint ]
• D. Cohen, L. Gauckler, E. Hairer, C. Lubich, Long-term analysis of numerical integrators for oscillatory Hamiltonian systems under minimal non-resonance conditions, BIT 55 (2015), 705-732.
  [ paper | preprint ]
• L. Gauckler, Error analysis of trigonometric integrators for semilinear wave equations, SIAM J. Numer. Anal. 53 (2015), 1082-1106.
  [ paper | preprint ]
• L. Gauckler, H. Yserentant, Regularity and approximability of the solutions to the chemical master equation, ESAIM Math. Model. Numer. Anal. 48 (2014), 1757-1775.
  [ paper | preprint ]
• E. Faou, L. Gauckler, C. Lubich, Plane wave stability of the split-step Fourier method for the nonlinear Schrödinger equation, Forum Math. Sigma 2 (2014), e5, 45 pp.
  [ paper | preprint ]
• L. Gauckler, E. Hairer, C. Lubich, Energy separation in oscillatory Hamiltonian systems without any non-resonance condition, Comm. Math. Phys. 321 (2013), 803-815.
  [ paper | preprint ]
• E. Faou, L. Gauckler, C. Lubich, Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus, Comm. Partial Differential Equations 38 (2013), 1123-1140.
  [ paper | preprint ]
• D. Cohen, L. Gauckler, One-stage exponential integrators for nonlinear Schrödinger equations over long times, BIT 52 (2012), 877-903.
  [ paper ]
• L. Gauckler, E. Hairer, C. Lubich, D. Weiss, Metastable energy strata in weakly nonlinear wave equations, Comm. Partial Differential Equations 37 (2012), 1391-1413.
  [ paper ]
• L. Gauckler, Convergence of a split-step Hermite method for the Gross-Pitaevskii equation, IMA J. Numer. Anal. 31 (2011), 396-415.
  [ paper ]
• L. Gauckler, C. Lubich, Splitting integrators for nonlinear Schrödinger equations over long times, Found. Comput. Math. 10 (2010), 275-302.
  [ paper ]
• L. Gauckler, C. Lubich, Nonlinear Schrödinger equations and their spectral semi-discretizations over long times, Found. Comput. Math. 10 (2010), 141-169.
  [ paper ]
• L. Gauckler, The Galois group of the Eisenstein polynomial X⁵+aX+a, Arch. Math. (Basel) 90 (2008), 136-139.
  [ paper ]

In conference proceedings

• L. Gauckler, E. Hairer, C. Lubich, Dynamics, numerical analysis, and some geometry, Proceedings of the International Congress of Mathematicians 2018, vol. 1, 453-485.
  [ paper | preprint ]
• L. Gauckler, On numerical energy conservation by the split-step Fourier method for the nonlinear Schrödinger equation, AIP Conf. Proc. 1738 (2016), 020004.
  [ paper ]
• L. Gauckler, Stability of plane waves in the nonlinear Schrödinger equation: analysis and numerics, in: Nonlinear evolution equations: analysis and numerics, Oberwolfach Rep. 11 (2014), 812-814.
  [ paper ]
• L. Gauckler, Long-time analysis of Hamiltonian partial differential equations and their discretizations, in: Geometric numerical integration, Oberwolfach Rep. 8 (2011), 851-853.
  [ paper ]
• J. Cernik, B. Schnaidt, L. Gauckler, D. Bartz, Curvilinear grid filtering by adaptive evaluation, Proceedings of SimVis 2007, 197-208.
• D. Bartz, B. Schnaidt, J. Cernik, L. Gauckler, J. Fischer, A. del Río, Volumetric high dynamic range windowing for better data representation, Proceedings of Afrigraph 2006, 137-144.
  [ paper | preprint ]

Manuscript

• L. Gauckler, High-order splitting integrators for nonlinear Schrödinger equations over long times, manuscript (2018), arXiv:1802.10324.
  [ preprint ]

Theses

• L. Gauckler, Geometric numerical integration of nonlinear Schrödinger and nonlinear wave equations, Habilitationsschrift (habilitation thesis), Technische Universität Berlin, 2017.
  [ thesis ]
• L. Gauckler, Long-time analysis of Hamiltonian partial differential equations and their discretizations, Dissertation (doctoral thesis), Universität Tübingen, 2010. urn:nbn:de:bsz:21-opus-47540.
  [ thesis ]