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Second-Order Flows for Approaching Stationary Points via the SAV-E Approach

  • Haifan Chen
  • Wei Liu
  • Ziqing Xie
  • Yifang Yuan
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Abstract

Second-order flows represent an emerging computational framework for approaching stationary points of variational energies, characterized by damped hyperbolic partial differential equations. In this paper, we develop a scalar auxiliary variable (SAV) method for this class of flows, referred to as SAV-E. The resulting scheme is linear and decoupled, and we prove unconditional modified-energy stability. We further establish subsequential convergence to stationary points for the Ginzburg-Landau and conserved Swift-Hohenberg models under suitable assumptions. Numerical experiments support the analysis and demonstrate robustness and efficiency compared with representative baselines and the corresponding gradient flows.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026secondorder,
  title = {{Second-Order Flows for Approaching Stationary Points via the SAV-E Approach}},
  author = {Haifan Chen and Wei Liu and Ziqing Xie and Yifang Yuan},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19884},
  eprint = {2610.19884},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19884},
}
RIS
TY  - UNPB
TI  - Second-Order Flows for Approaching Stationary Points via the SAV-E Approach
AU  - Haifan Chen
AU  - Wei Liu
AU  - Ziqing Xie
AU  - Yifang Yuan
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19884
UR  - https://arxiv.org/abs/2610.19884
AB  - Second-order flows represent an emerging computational framework for approaching stationary points of variational energies, characterized by damped hyperbolic partial differential equations. In this paper, we develop a scalar auxiliary variable (SAV) method for this class of flows, referred to as SAV-E. The resulting scheme is linear and decoupled, and we prove unconditional modified-energy stability. We further establish subsequential convergence to stationary points for the Ginzburg-Landau and conserved Swift-Hohenberg models under suitable assumptions. Numerical experiments support the analysis and demonstrate robustness and efficiency compared with representative baselines and the corresponding gradient flows.
ER  -