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<p>In this paper, an iterative two-level (ITL) algorithm for the finite element discretization of nonsymmetric or indefinite elliptic problems is analyzed. Compared with the existing iterative two-grid (ITG) algorithm, only one layer of physical grid, which is easier to apply on unstructured grids, is utilized in our algorithm. The same coarse grid space is used in both algorithms, but the high-order finite element space on the coarse grid, which requires fewer mesh degrees of freedom, is used as the “fine” grid space in the ITL algorithm. Theoretical analysis indicates that three variables, namely the polynomial degrees <i>s</i> and <i>r</i> of the coarse and “fine” grid spaces, and the iteration number <i>k</i>, are included in the convergence order of the ITL algorithm, while two variables, namely the polynomial degree <i>l</i> and the iteration number <i>k</i>, are included in the convergence order of the ITG algorithm. Hence, the ITL algorithm has more parameter combinations when the same convergence order is reached by both algorithms. Numerical experiments also show that with appropriate combinations of <i>s</i>, <i>r</i>, and <i>k</i>, the computational time of the ITL algorithm is significantly less than that of the ITG algorithm when the same error accuracy is achieved.</p>

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Convergence Analysis of Iterative Two-Level Algorithm for Nonsymmetric or Indefinite Elliptic Problems

  • 期刊论文

  • 发表日期：

    2026年3月31日

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  • Ming Tang,
  • Feng Jiao,
  • Minli Zeng,
  • Liuqiang Zhong

摘要

In this paper, an iterative two-level (ITL) algorithm for the finite element discretization of nonsymmetric or indefinite elliptic problems is analyzed. Compared with the existing iterative two-grid (ITG) algorithm, only one layer of physical grid, which is easier to apply on unstructured grids, is utilized in our algorithm. The same coarse grid space is used in both algorithms, but the high-order finite element space on the coarse grid, which requires fewer mesh degrees of freedom, is used as the “fine” grid space in the ITL algorithm. Theoretical analysis indicates that three variables, namely the polynomial degrees s and r of the coarse and “fine” grid spaces, and the iteration number k, are included in the convergence order of the ITL algorithm, while two variables, namely the polynomial degree l and the iteration number k, are included in the convergence order of the ITG algorithm. Hence, the ITL algorithm has more parameter combinations when the same convergence order is reached by both algorithms. Numerical experiments also show that with appropriate combinations of s, r, and k, the computational time of the ITL algorithm is significantly less than that of the ITG algorithm when the same error accuracy is achieved.