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arXiv · 2402.11266

Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates

Lun Ji·Hang Li·Alexander Ostermann·Chunmei Su
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Abstract

We investigate a filtered Lie-Trotter splitting scheme for the ``good" Boussinesq equation and derive an error estimate for initial data with very low regularity. Through the use of discrete Bourgain spaces, our analysis extends to initial data in $H^{s}$ for $0 1/2$ imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order $\tau^{s/2}$ in $L^2$ for such levels of regularity. Our analytical findings are supported by numerical experiments.

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Lun Ji, Hang Li, Alexander Ostermann, Chunmei Su. 2024-02-17. Filtered Lie-Trotter splitting for the "good" Boussinesq equation: low regularity error estimates. https://doi.org/10.1090/mcom/4023

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