2021/07/28 by Li, Buyang, Ma, Shu, Schratz, Katharina · 1 citation
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2107.13427
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→ 0.