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

2024/02/17 by Lun Ji, Hang Li, Ji, Lun +5 · 1 citation
Mathematics · Engineering · #Advanced Mathematical Physics Problems #Numerical methods for differential equations #Computational Fluid Dynamics and Aerodynamics

paper · pdf · doi:10.48550/arxiv.2402.11266

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 01/2 imposed by the bilinear estimate in smooth Sobolev spaces. We establish convergence rates of order τ^s/2 in L² for such levels of regularity. Our analytical findings are supported by numerical experiments.

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