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<p>This paper aims to develop a robust nonconforming finite element method for a strain gradient elastic model which is a singularly perturbed fourth-order problem with a small size parameter. By means of Nitsche’s technique, we treat all boundary conditions weakly through the penalty technique. For locking-free analysis, we construct several weak interpolation operators possessing a commutative relation. Then we can derive the optimal and uniform error estimates with respect to both the size parameter and the Lamé constant under some assumptions. Some numerical experiments verify the theoretical findings.</p>

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A Nonconforming Finite Element Method with the Use of Nitsche’s Technique for a Strain Gradient Elastic Model

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Mingqing Chen,
  • Jianguo Huang,
  • Xuehai Huang

摘要

This paper aims to develop a robust nonconforming finite element method for a strain gradient elastic model which is a singularly perturbed fourth-order problem with a small size parameter. By means of Nitsche’s technique, we treat all boundary conditions weakly through the penalty technique. For locking-free analysis, we construct several weak interpolation operators possessing a commutative relation. Then we can derive the optimal and uniform error estimates with respect to both the size parameter and the Lamé constant under some assumptions. Some numerical experiments verify the theoretical findings.