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<p>We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation and terminates in linear time with respect to the number of initial vertices. We show that Maubach’s routine with this initialization always terminates and generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.</p>

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Adaptive Mesh Refinement for Arbitrary Initial Triangulations

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2025年3月24日

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  • Lars Diening,
  • Lukas Gehring,
  • Johannes Storn

摘要

We introduce a simple initialization of the Maubach bisection routine for adaptive mesh refinement which applies to any conforming initial triangulation and terminates in linear time with respect to the number of initial vertices. We show that Maubach’s routine with this initialization always terminates and generates meshes that preserve shape regularity and satisfy the closure estimate needed for optimal convergence of adaptive schemes. Our ansatz allows for the intrinsic use of existing implementations.