Year: 2021
Type: preprint
Abstract: A new type of low-regularity integrator is proposed for Navier-Stokes equations, coupled with a stabilized finite element method in space. Unlike the other low-regularity integrators for nonlinear dispersive equations, which are all fully explicit in time, the proposed method is semi-implicit in time in order to preserve the energy-decay structure of NS equations. First-order convergence of the proposed method is established independent of the viscosity coefficient $μ$, under weaker regularity conditions than other existing numerical methods, including the semi-implicit Euler method and classical exponential integrators. Numerical results show that the proposed method is more accurate than the semi-implicit Euler method in the viscous case $μ=O(1)$, and more accurate than the classical exponential integrator in the inviscid case $μ\rightarrow 0$.
Source: arXiv (Cornell University)
Authors: Li, Buyang, Ma, Shu, Schratz, Katharina
Language: English
Subfield: Numerical Analysis
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
Award: G7802200530
OpenAlex ID: W3186562167