2023/05/18 by Dominic Breit, Breit, Dominic, Thamsanqa Castern Moyo +4 · 1 citation
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2305.10999
openalex publication_date 2023/05/18 · openalex created_date 2023/05/21 · openalex updated_date 2026/07/28
We study the 2D Navier-Stokes equation with transport noise subject to periodic boundary conditions. Our main result is an error estimate for the time-discretisation showing a convergence rate of order (up to) 1/2. It holds with respect to mean square error convergence, whereas previously such a rate for the stochastic Navier-Stokes equations was only known with respect to convergence in probability. Our result is based on uniform-in-probability estimates for the continuous as well as the time-discrete solution exploiting the particular structure of the noise. Eventually, we perform numerical simulations for the corresponding problem on bounded domains with no-slip boundary conditions. They suggest the same convergence rate as proved for the periodic problem hinging sensitively on the compatibility of the data. We also compare the energy profiles with those for corresponding problems with additive or multiplicative Itô-type noise.