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<p>In this paper, we propose a stabilized parallel splitting algorithm for the Biot model. Unlike sequential solving, our method enables parallel computation of the subequation about elasticity and parabolic problem. By introducing appropriate stabilizers, we prove that the algorithm is unconditionally energy-stable and robust to material parameters. The displacement is approximated using an <i>H</i>(div)-conforming finite element space, while the pressure is discretized with piecewise linear elements. Consequently, our method avoids locking while maintaining unconditional energy stability. We conducted error analysis, and performed numerical experiments to demonstrate the method’s efficiency.</p>

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Unconditionally Energy-Stable and Locking-Free Parallel Splitting Finite Element Method for the Biot Model

  • 期刊论文

  • 发表日期：

    2025年7月12日

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  • Jijing Zhao,
  • Huangxin Chen,
  • Shuyu Sun,
  • Hongpeng Li

摘要

In this paper, we propose a stabilized parallel splitting algorithm for the Biot model. Unlike sequential solving, our method enables parallel computation of the subequation about elasticity and parabolic problem. By introducing appropriate stabilizers, we prove that the algorithm is unconditionally energy-stable and robust to material parameters. The displacement is approximated using an H(div)-conforming finite element space, while the pressure is discretized with piecewise linear elements. Consequently, our method avoids locking while maintaining unconditional energy stability. We conducted error analysis, and performed numerical experiments to demonstrate the method’s efficiency.