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<p>Scalar auxiliary variable (SAV) methods are a class of linear schemes for solving gradient flows that are known for the stability of a ‘modified’ energy. In this paper, we propose an improved SAV (iSAV) scheme that not only retains the complete linearity but also ensures rigorously the stability of the original energy. The convergence and optimal error bound are rigorously established for the iSAV scheme and discussions are made for its high-order extension. Extensive numerical experiments are done to validate the convergence, robustness and energy stability of iSAV, and some comparisons are made.</p>

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Improved Scalar Auxiliary Variable Schemes for Original Energy Stability of Gradient Flows

  • 期刊论文

  • 发表日期：

    2025年2月28日

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  • Rui Chen,
  • Tingfeng Wang,
  • Xiaofei Zhao

摘要

Scalar auxiliary variable (SAV) methods are a class of linear schemes for solving gradient flows that are known for the stability of a ‘modified’ energy. In this paper, we propose an improved SAV (iSAV) scheme that not only retains the complete linearity but also ensures rigorously the stability of the original energy. The convergence and optimal error bound are rigorously established for the iSAV scheme and discussions are made for its high-order extension. Extensive numerical experiments are done to validate the convergence, robustness and energy stability of iSAV, and some comparisons are made.