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<p>In this paper, we introduce two novel numerical schemes for a droplet model, employing a new Lagrange multiplier method. These schemes, encompassing both first and second order accurate temporal algorithms, are specifically designed to address the complex nonlinearity and inherent singularity of the model, commonly encountered in physical and engineering applications. A key feature of our approach is the unconditional energy dissipation, allowing for unrestricted time step sizes, which is critical for efficiently simulating the extended coarsening processes. The crux of these schemes involves solving a nonlinear algebraic equation to determine the Lagrange multiplier, a technique that represents a significant advancement in this field. We have conducted a few numerical experiments to validate the effectiveness and accuracy of our proposed methods. These include rigorous tests on convergence and energy reduction, affirming the robustness and precision of our algorithms.</p>

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Stabilized numerical schemes for a droplet model based on a new Lagrange multiplier approach

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Juan Zhang,
  • Maoqin Yuan,
  • Jianxiong Cao

摘要

In this paper, we introduce two novel numerical schemes for a droplet model, employing a new Lagrange multiplier method. These schemes, encompassing both first and second order accurate temporal algorithms, are specifically designed to address the complex nonlinearity and inherent singularity of the model, commonly encountered in physical and engineering applications. A key feature of our approach is the unconditional energy dissipation, allowing for unrestricted time step sizes, which is critical for efficiently simulating the extended coarsening processes. The crux of these schemes involves solving a nonlinear algebraic equation to determine the Lagrange multiplier, a technique that represents a significant advancement in this field. We have conducted a few numerical experiments to validate the effectiveness and accuracy of our proposed methods. These include rigorous tests on convergence and energy reduction, affirming the robustness and precision of our algorithms.