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arXiv · 2610.05045

A second-order energy-stable low-regularity integrator for the Navier--Stokes equations

Shu Ma
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Abstract

A second-order exponential low-regularity integrator is proposed for the incompressible Navier--Stokes equations. The method requires only linear solves and satisfies a discrete energy-decay property. Second-order temporal convergence is established under a uniform $H^4$ solution bound, with an error constant that remains bounded as the viscosity tends to zero. For the Fourier--Galerkin discretization, the optimal spatial convergence rate is established for fixed viscosity. The method can also be extended to conforming finite element methods while retaining the discrete energy-decay structure. Numerical results confirm the convergence orders and robustness with respect to the viscosity.

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Shu Ma. 2026-10-04. A second-order energy-stable low-regularity integrator for the Navier--Stokes equations. https://arxiv.org/abs/2610.05045

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