Scholarlink

<p>We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models.</p><p>We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Fitted norm preconditioners for the Hodge-Laplacian in mixed form

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年12月1日

查看全文
  • Wietse M. Boon,
  • Johannes Kraus,
  • Tomáš Luber,
  • Maria Lymbery

摘要

We use the practical framework for abstract perturbed saddle-point problems recently introduced by Hong et al. to analyze the mixed formulation of the Hodge-Laplace problem on a Hilbert complex. We compose two parameter-dependent norms in which the uniform continuity and stability of the problem follow. This not only guarantees the well-posedness of the corresponding variational formulation on the continuous level, but also of related compatible discrete models.

We further simplify the obtained norms and, in both cases, arrive at the same norm-equivalent preconditioner that is easily implementable. The efficiency and uniformity of the preconditioner are demonstrated numerically by the fast convergence and uniformly bounded number of preconditioned MinRes iterations required to solve various instances of Hodge-Laplace problems in two and three space dimensions.