Katharina Schratz
Professor at Sorbonne University
Laboratoire Jacques-Louis Lions
Sorbonne Université
4 place Jussieu, 75005 Paris cedex 05
office: 15-16 312
email: katharina.schratz@sorbonne-universite.fr

group22
(Yue, Malika, Katharina, Yvonne, María)
logoljll LOGO_ERC
Ongoing projects

ERC Starting Grant LAHACODE
Low-regularity and high oscillations: numerical analysis and computation of dispersive evolution equations
2020 - 2025 (financed by the European Research Council)
https://cordis.europa.eu/project/id/850941

Plenary talks

FoCM 2023 conference (2023)

30 Years of Acta Numerica (2022)

NUMDIFF 16 (2021)

40th European Dynamic Days Conference (2021)

SciCADE (2019)

Editorial boards (associated editor)

SIAM Journal on Numerical Analysis (SINUM) (since 2023)

https://www.siam.org/publications/journals/siam-journal-on-numerical-analysis-sinum

IMA Journal of Numerical Analysis (since 2021)

https://academic.oup.com/imajna

Advances in Continuous and Discrete Models: Theory and Modern Applications (since 2021)

https://advancesindifferenceequations.springeropen.com

Acta Applicandae Mathematicae (since 2021)

https://www.springer.com/journal/10440

Organsiation of workshops

Modern methods for differential equations of quantum mechanics

Banff International Research Station, Banff (Canada) 2024

Women in nonlinear dispersive PDEs

Banff International Research Station, Banff (Canada) 2023

Normal forms and splitting methods

13-17 June 2022, Pornichet (France)

Computational Mathematics for Quantum Technologies

1-5 August 2022, Bath (UK)

Recorded talks

Séminaire du LJLL 2020

Resonances as a computational tool

MSRI Introductory Workshop: Mathematical problems in fluid dynamics 2021

Introduction to time discretisation of some nonlinear PDEs (at low regularity)

One World Numerical Analysis: ICMS 2022

Resonances as a computational tool

Publications

Y. Feng, G. Maierhofer, K. Schratz, Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
https://arxiv.org/abs/2302.00383 (preprint 2023)
L. Ji, A. Ostermann, F. Rousset, K. Schratz, Low regularity error estimates for the time integration of 2D NLS
https://arxiv.org/abs/2301.10639 (preprint 2023)
Y. Feng, K. Schratz, Improved uniform error bounds on a Lawson-type exponential integrator for the long-time
dynamics of sine-Gordon equation

https://arxiv.org/abs/2211.09402 (preprint 2022)
V. Banica, G. Maierhofer, K. Schratz, Numerical integration of Schrödinger maps via the Hasimoto transform
https://arxiv.org/abs/2211.01282 (preprint 2022)
G. Maierhofer, K. Schratz, Bridging the gap: symplecticity and low regularity on the example of the KdV equation
https://arxiv.org/abs/2205.05024 (preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz, Approximations of dispersive PDEs in the presence of low-regularity randomness
https://arxiv.org/abs/2205.02156 (preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz, Low regularity integrators via decorated trees
https://arxiv.org/abs/2202.01171 (preprint 2022)
K. Kropielnicka, K. Lademann, K. Schratz Effective high order integrators for
low to highly oscillatory Klein-Gordon equations
(preprint 2021)
A. Iserles, K. Kropielnicka, K. Schratz, M. Webb. Solving the linear Schrödinger equation on the real line
http://arxiv.org/abs/2102.00413 (preprint 2021)
C.-K. Doan, T.-T.-P. Hoang, K. Schratz, Low regularity integrators for semilinear parabolic equations
with maximum bound principles

BIT Numer Math (to appear) https://link.springer.com/article/10.1007/s10543-023-00946-2
B. Li, K. Schratz, F. Zivcovich, A second-order low-regularity correction of Lie splitting for the
semilinear Klein-Gordon equation

M2AN (to appear) http://arxiv.org/abs/2203.15539
B. Li, S. Ma, K. Schratz, A semi-implicit low-regularity integrator for Navier-Stokes equations
SIAM J. Numer. Anal. (to appear) http://arxiv.org/abs/2107.13427
M. Cabrera Calvo, K. Schratz. Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony
equation with dispersive parameter

BIT Numer Math (to appear) http://arxiv.org/abs/2105.03732
M. Cabrera Calvo, F. Rousset, K. Schratz. Time integrators for dispersive equations in the long wave regime
Math. Comp. (to appear) http://arxiv.org/abs/2105.03731
M. Cabrera Calvo, K. Schratz. Uniformly accurate low regularity integrators for the Klein-Gordon equation
from the classical to non-relativistic limit regime

SIAM J. Numer. Anal. (to appear) http://arxiv.org/abs/2104.11672
F. Rousset, K. Schratz. Convergence error estimates at low regularity for time discretizations of KdV
Pure and Applied Analysis (to appear) https://arxiv.org/abs/2102.11125
Y. Bruned, K. Schratz. Resonance based schemes for dispersive equations via decorated trees
Forum of Mathematics, Pi 10:e2 1-76 (2022) doi:10.1017/fmp.2021.13
A. Poulain, K. Schratz. Convergence, error analysis and longtime behavior of the Scalar Auxiliary
Variable method for the nonlinear Schrödinger equation

IMA J. Numer. Anal. (to appear) https://arxiv.org/abs/2012.13943
A. Ostermann, F. Rousset, K. Schratz. Error estimates at low regularity of splitting schemes for NLS
Math. Comp. (to appear) https://arxiv.org/abs/2012.14146
F. Rousset, K. Schratz. A general framework of low regularity integrators
SIAM J. Numer. Anal. 59:1735-1768 (2021) http://arxiv.org/abs/2010.01640
A. Ostermann, F. Rousset, K. Schratz. Fourier integrator for periodic NLS: low regularity estimates via discrete Bourgain spaces
J. Eur. Math. Soc. (JEMS) (to appear) http://arxiv.org/abs/2006.12785
K. Schratz, Y. Wang, X. Zhao. Low-regularity integrators for nonlinear Dirac equations.
Math. Comp. 90:189-214 (2021) https://arxiv.org/abs/1906.09413
A. Ostermann, F. Rousset, K. Schratz. Error estimates of a Fourier integrator for the cubic Schrödinger equation at low regularity.
Found. Comput. Math. 21:725-765 (2021) doi 10.1007/s10208-020-09468-7
M. Hofmanová, M. Knöller, K. Schratz. Randomized exponential integrators for modulated non-linear Schrödinger equations.
IMA J. Numer. Anal. 40:2143-2162 (2020) https://doi.org/10.1093/imanum/drz050
S. Baumstark, K. Schratz. Asymptotic preserving integrators for the quantum Zakharov system.
BIT Numer Math (2020) doi:10.1007/s10543-020-00815-2
M. Knöller, A. Ostermann, K. Schratz. A Fourier integrator for the cubic nonlinear Schrödinger equation with rough initial data.
SIAM J. Numer. Anal. 57:1967-1986 (2019) doi/10.1137/18M1198375
S. Baumstark, K. Schratz. Oscillatory integrators for Klein-Gordon-Zakharov systems from low-to high-plasma frequency regimes.
SIAM J. Numer. Anal. 57:429-457 (2019) doi:10.1137/18M1177184
L. Gauckler, J. Lu, J. Marzuola, F. Rousset, K. Schratz. Trigonometric integrators for quasilinear wave equations.
Math. Comp.
88:717-749 (2019) doi/10.1090/mcom/3339
P. Krämer, K. Schratz, X. Zhao. Splitting Methods for Nonlinear Dirac Equations with Thirring type
interaction in the Nonrelativistic Limit Regime.

J. Comput. Appl. Math. 112494, 2019. Online first doi:10.1016/j.cam.2019.112494
K. Schratz, X. Zhao. On the comparison of the asymptotic expansion techniques for the nonlinear Klein-Gordon
equation in the non relativistic limit regime.
DCDS-B 2019. Online first doi:10.3934/dcdsb.2020043
S. Baumstark, G. Schneider, K. Schratz, D. Zimmermann. Effective slow dynamics models for a class of dispersive systems.
J. Dyn. Diff. Equat. 2019. Online first doi:10.1007/s10884- 019-09791-w
A. Ostermann, K. Schratz. Low regularity exponential-type integrators for semilinear Schrödinger equations.
Found. Comput. Math. 18:731-755 (2018) doi/10.1007/s10208-017-9352-1
S. Baumstark, E. Faou, K. Schratz. Uniformly accurate exponential-type integrators for Klein-Gordon equations
with asymptotic convergence to the classical NLS splitting

Math. Comp. 87:1227-1254 (2018) doi:10.1090/mcom/3263
M. Hofmanová, K. Schratz. An exponential-type integrator for the KdV equation.
Numer. Math. 136:1117-1137 (2017) doi:10.1007/s00211-016-0859-1
S. Baumstark, G. Kokkala, K. Schratz. Asymptotic consistent exponential-type integrators for Klein-Gordon-
Schrödinger systems from relativistic to non-relativistic regimes.

ETNA 48:63-80 (2018) doi:10.1553/etna vol48s63
S. Herr, K. Schratz . Trigonometric time integrators for the Zakharov system.
IMA J. Numer. Anal. 37:2042-2066 (2017) doi: 10.1093/imanum/drw059
P. Krämer, K. Schratz . Efficient time integration of Maxwell-Klein-Gordon system in the non-relativistic limit regime.
J. Comput. Appl. Math. 316:247-259 (2017) doi:10.1016/j.cam.2016.07.007
M. Daub, G. Schneider, K. Schratz. From the Klein-Gordon-Zakharov system to the Klein-Gordon equation.
Math. Meth. Appl. Sci. 39:5371-5380 (2016) doi:10.1002/mma.3922
J. Eilinghoff, R. Schnaubelt, K. Schratz. Fractional error estimates of splitting schemes for the nonlinear Schrödinger equation.
J. Math. Anal. Appl. 442:740-760 (2016) doi:10.1016/j.jmaa.2016.05.014
E. Hansen, A. Ostermann, K. Schratz. The error structure of the Douglas-Rachford splitting method for stiff linear problems.
J. Comput. Appl. Math. 303:140-145 (2016) doi:10.1016/j.cam.2016.02.037
E. Faou, A. Ostermann, K. Schratz. Analysis of exponential splitting methods for inhomogeneous parabolic equations.
IMA J. Numer. Anal. 35:161-178 (2015) doi:doi.org/10.1093/imanum/dru002
E. Faou, K. Schratz. Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime.
Numer. Math. 126:441-469 (2014) doi:10.1007/s00211-013-0567-z
A. Ostermann, K. Schratz. Stability of exponential operator splitting methods for non-contractive semigroups.
SIAM J. Numer. Anal. 51:191-203 (2013) doi:10.1137/110846580
M. Mergili, K. Schratz, A. Ostermann, W. Fellin. A GRASS GIS Implementation of the Savage-Hutter Avalanche Model and
Its Application to the 1987 Val Pola Event.

Landslide Science and Practice. 3:367-373 (2013) doi:10.1007/978-3-642-31310-3_50
A. Ostermann, K. Schratz. Error analysis of splitting methods for inhomogeneous evolution equa- tions.
Appl. Numer. Math. 62:1436-1446 (2012) doi:10.1016/j.apnum.2012.06.002
M. Mergili, K. Schratz, A. Ostermann, W. Fellin. Physically-based modelling of granular flows with Open Source GIS.
Nat. Hazards Earth Syst. Sci. 12:187-200 (2012) doi:10.5194/nhess-12-187-2012

Supervision

2022- : Yue Feng, Post-doc, Sorbonne Université, France
Sep 2021- : Georg Maierhofer, Post-doc, Sorbonne Université, France
2021-2022 : Nikola Stoilov, Post-doc, Sorbonne Université, France
2021-2022 : Franco Zivcovich, Post-doc, Sorbonne Université, France
2018-2019 : Simon Baumstark, Post-doc, KIT, Allemagne
2017-2018 : Patrick Krämer, Post-doc, KIT, Allemagne
2018-2019 : Xiaofei Zhao, Post-doc, KIT, Allemagne
Sep 2021- : Yvonne Bronsard Alama, Thèse de doctorat, Sorbonne Université, France
Nov 2020- : María Cabrera Calvo, Thèse de doctorat, Sorbonne Université, France
2015-2018 : Simon Baumstark, Thèse de doctorat, KIT, Allemagne
2014-2017 : Patrick Krämer, Thèse de doctorat, KIT, Allemagne
2021 : Yvonne Bronsard Alama, Stage, Sorbonne Université, France
2017-2018 : Jelena Stjepanovic, Master, KIT, Allemagne
2017-2018 : Irina Wetteborn, Master, KIT, Allemagne
2017-2018 : Jan Bohn, Master, KIT, Allemagne
2016-2017 : Georgia Kokkala, Master, KIT, Allemagne
2014-2015 : Simon Baumstark, Master, KIT, Allemagne
2013-2014 : Patrick Krämer, Master (co-advisor), KIT, Allemagne
2011-2012 : Tobias Hell, Master (co-advisor), Université d'Innsbruck, Autriche
2011-2012 : Georg Spielberger, Master (co-advisor), Université d'Innsbruck, Autriche