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<p>We propose a mixed formulation along with a regularization method to solve the Poisson equation under the Tresca friction law, and we provide a rigorous theoretical analysis, including the well-posedness and the error estimates on regularization parameter (and mesh size for discretization), in both continuous and discrete settings. We design two iteration algorithms to solve the discrete mixed regularization problem, and investigate the convergence. Several numerical experiments are conducted to verify the theoretical convergence rates and the effectiveness of the proposed algorithms.</p>

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The mixed regularization method for the Poisson equation with the Tresca frictional boundary condition

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Zihan Liu,
  • Jingyan Hu,
  • Ping Zeng,
  • Guanyu Zhou

摘要

We propose a mixed formulation along with a regularization method to solve the Poisson equation under the Tresca friction law, and we provide a rigorous theoretical analysis, including the well-posedness and the error estimates on regularization parameter (and mesh size for discretization), in both continuous and discrete settings. We design two iteration algorithms to solve the discrete mixed regularization problem, and investigate the convergence. Several numerical experiments are conducted to verify the theoretical convergence rates and the effectiveness of the proposed algorithms.