ERC project : LAHACODE

logoljll LOGO_ERC
ERC Starting Grant : LAHACODE

Low-regularity and high oscillations: numerical analysis and
computation of dispersive evolution equations
Funding period: 2020 - 2025
(financed by the European Research Council)
Members :
Yvonne Bronsard Alama
María Cabrera Calvo
Albert Cohen
Yue Feng
Katharina Schratz

Former Members :
Georg Maierhofer
Nikola Stoilov
Franco Zivcovich

Publications :

Y. Feng, K. Schratz, Improved uniform error bounds on a Lawson-type exponential integrator for the long-time
dynamics of sine-Gordon equation (preprint 2022)
V. Banica, G. Maierhofer, K. Schratz, Numerical integration of Schrödinger maps via the Hasimoto transform (preprint 2022)
G. Maierhofer, K. Schratz, Bridging the gap: symplecticity and low regularity on the example of the KdV equation (preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz, Approximations of dispersive PDEs in the presence of low-regularity randomness (preprint 2022)
B. Li, K. Schratz, F. Zivcovich, A second-order low-regularity correction of Lie splitting for the
semilinear Klein-Gordon equation

M2AN(to appear)
C.-K. Doan, T.-T.-P. Hoang, K. Schratz, Low regularity integrators for semilinear parabolic equations
with maximum bound principles
(preprint 2022)
Y. A. Bronsard, Y. Bruned, K. Schratz, Low regularity integrators via decorated trees (preprint 2022)
M. Caliari, F. Cassini, F. Zivcovich,
A μ-mode BLAS approach for multidimensional tensor-structured problems (preprint 2021)
M. Caliari, F. Cassini, L. Einkemmer, A. Ostermann, F. Zivcovich,
A μ-mode integrator for solving evolution equations in Kronecker form (preprint 2021)
Y. Alama Bronsard Error analysis of a class of semi-discrete schemes for solving the Gross-Pitaevskii equation at low regularity J. Comp. App. Math, 114632, July 202
M. Cabrera Calvo Uniformly accurate integrators for Klein-Gordon-Schrödinger systems from the
classical to non-relativistic limit regime to appear in Journal of Computational and Applied Mathematics
G. Maierhofer, D. Huybrechs, An analysis of least-squares oversampled collocation methods for
compactly perturbed boundary integral equations in two dimensions (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 (preprint 2021)
B. Li, S. Ma, K. Schratz, A semi-implicit low-regularity integrator for Navier-Stokes equations to appear in SIAM J. Numer. Anal.
M. Cabrera Calvo, K. Schratz. Uniformly accurate splitting schemes for the Benjamin-Bona-Mahony
equation with dispersive parameter to appear in BIT Numer Math
M. Cabrera Calvo, F. Rousset, K. Schratz. Time integrators for dispersive equations in the long wave regime to appear in Math. Comp.
M. Cabrera Calvo, K. Schratz. Uniformly accurate low regularity integrators for the classical to non-relativistic limit regime to appear in SIAM J. Numer. Anal.
F. Rousset, K. Schratz. Convergence error estimates at low regularity for time discretizations of KdV to appear in Pure and Applied Analysis
Y. Bruned, K. Schratz. Resonance based schemes for dispersive equations via decorated trees
doi:10.1017/fmp.2021.13 Forum of Mathematics, Pi 10:e2 1-76 (2022)
A. Poulain, K. Schratz. Convergence, error analysis and longtime behavior of the Scalar Auxiliary
Variable method for the nonlinear Schrödinger equation to appear in IMA J. Numer. Anal.
A. Ostermann, F. Rousset, K. Schratz. Error estimates at low regularity of splitting schemes for NLS to appear in Math. Comp.
F. Rousset, K. Schratz. A general framework of low regularity integrators SIAM J. Numer. Anal. 59:1735-1768 (2021)
A. Ostermann, F. Rousset, K. Schratz. Fourier integrator for periodic NLS:
low regularity estimates via discrete Bourgain spaces to appear in J. Eur. Math. Soc. (JEMS)
K. Schratz, Y. Wang, X. Zhao. Low-regularity integrators for nonlinear Dirac equations.
Math. Comp. 90:189-214 (2021)
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)
S. Baumstark, K. Schratz. Asymptotic preserving integrators for the quantum Zakharov system.
doi:10.1007/s10543-020-00815-2 BIT Numer Math (2020)