Katharina Schratz
Professor at Sorbonne University
Laboratoire Jacques-Louis Lions
Sorbonne Université
4 place Jussieu, 75005 Paris France
office: 15-16 312

logoljll LOGO_ERC
(Malika, Franco, María, Katharina, Yvonne, Georg)
• Projects (ongoing):

LAHACODE (ERC Starting Grant)
Low-regularity and high oscillations:
numerical analysis and computation of dispersive evolution equations
2020 - 2025 (funded by European Research Council)

• Editorial boards

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


IMA Journal of Numerical Analysis (since 2021)


Acta Applicandae Mathematicae (since 2021)


• Plenary talks

GAMM 2025

Biennial Conference in Numerical Analysis 2025

Cedya 2024

Mathematics Muenster Mid-term Conference (2024)

Symposium on Sparsity and Singular Structures (2024)

FoCM 2023

NUMDIFF 16 (2021)

40th European Dynamic Days (2021)

SciCADE (2019)

• 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

June 2022, Pornichet (France)

Computational Mathematics for Quantum Technologies

August 2022, Bath (UK)

• Recorded talks

Institute for Advanced Study: Analysis and Mathematical Physics seminar

Resonances as a computational tool

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

J. Rowbottom, G. Maierhofer, T. Deveney, K. Schratz, P. Lio, CB Schönlieb, C. Budd, G-Adaptive mesh refinement -- leveraging graph neural networks and differentiable finite element solvers
https://arxiv.org/abs/2407.04516 (preprint)
T. Jin, G. Maierhofer, K. Schratz, Y. Xiang, A fast neural hybrid Newton solver adapted to implicit methods for nonlinear dynamics
https://arxiv.org/abs/2407.03945 (preprint)
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)
Y. A. Bronsard, Y. Bruned, K. Schratz, Low regularity integrators via decorated trees
https://arxiv.org/abs/2202.01171 (preprint)
A. Iserles, K. Kropielnicka, K. Schratz, M. Webb, Solving the linear Schrödinger equation on the real line
http://arxiv.org/abs/2102.00413 (preprint)
L. Ji, A. Ostermann, F. Rousset, K. Schratz, Low regularity error estimates for the time integration of 2D NLS
IMA J. Numer. Anal. (to appear) https://arxiv.org/abs/2301.10639
F. Rousset, K. Schratz, Resonances as a computational tool
Found. Comput. Math. (to appear) https://arxiv.org/abs/2405.10572
Y. Feng, K. Schratz, Improved uniform error bounds on a Lawson-type exponential integrator for the long-time dynamics of sine-Gordon equation
Numer. Math. (to appear) https://arxiv.org/abs/2211.09402
L. Ji, A. Ostermann, F. Rousset, K. Schratz, Low regularity full error estimates for the cubic nonlinear Schrödinger equation
SIAM J. Numer. Anal (to appear) https://arxiv.org/abs/2311.14366
Y. Feng, G. Maierhofer, K. Schratz, Long-time error bounds of low-regularity integrators for nonlinear Schrödinger equations
Math. Comp. (to appear) https://arxiv.org/abs/2302.00383
V. Banica, G. Maierhofer, K. Schratz, Numerical integration of Schrödinger maps via the Hasimoto transform
SIAM J. Numer. Anal. (to appear) https://arxiv.org/abs/2211.01282
Y. A. Bronsard, Y. Bruned, K. Schratz, Approximations of dispersive PDEs in the presence of low-regularity randomness
Found. Comput. Math. (to appear) https://arxiv.org/abs/2205.02156
C.-K. Doan, T.-T.-P. Hoang, L. Ju, 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 57:899-919 (2023) 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. 60:2273-2292 (2022) 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 60:888-912 (2022) 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. Math. Comp. 91:2197-2214 (2021) 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. 60:888-912 (2022) 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 4:127-152 (2022) 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. 91:169-182 (2022) 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) 25:3913-3952 (2022) 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
2022-2023 : Yue Feng, Post-doc, Sorbonne Université, France
2021-2023 : 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
2021-2024 : Yvonne Bronsard Alama, PhD student, Sorbonne Université, France
2020-2023 : María Cabrera Calvo, PhD student, Sorbonne Université, France
2015-2018 : Simon Baumstark, PhD student, KIT, Allemagne
2014-2017 : Patrick Krämer, PhD student, KIT, Allemagne
2024 : Chengewei Fan, Master student, Sorbonne Université, France
2023 : Qinyan Zhou, Master student, Sorbonne Université, France
2021 : Yvonne Bronsard Alama, Master student, Sorbonne Université, France
2017-2018 : Jelena Stjepanovic, Master student, KIT, Allemagne
2017-2018 : Irina Wetteborn, Master student, KIT, Allemagne
2017-2018 : Jan Bohn, Master student, KIT, Allemagne
2016-2017 : Georgia Kokkala, Master student, KIT, Allemagne
2014-2015 : Simon Baumstark, Master student, KIT, Allemagne
2013-2014 : Patrick Krämer, Master student (co-advisor), KIT, Allemagne
2011-2012 : Tobias Hell, Master student (co-advisor), Université d'Innsbruck, Autriche
2011-2012 : Georg Spielberger,Master student (co-advisor), Université d'Innsbruck, Autriche