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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 H4 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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Cite

BibTeXRIS
BibTeX
@misc{ma2026secondorder,
  title = {{A second-order energy-stable low-regularity integrator for the Navier--Stokes equations}},
  author = {Shu Ma},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.05045},
  eprint = {2610.05045},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.05045},
}
RIS
TY  - UNPB
TI  - A second-order energy-stable low-regularity integrator for the Navier--Stokes equations
AU  - Shu Ma
PY  - 2026
DA  - 2026/10/04
PB  - arXiv
DO  - 10.48550/arxiv.2610.05045
UR  - https://arxiv.org/abs/2610.05045
AB  - 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.
ER  -