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A coarsening algorithm on adaptive red-green-blue refined meshes
Numerical Algorithms ( IF 2.1 ) Pub Date : 2020-10-01 , DOI: 10.1007/s11075-020-01003-7
Stefan A. Funken , Anja Schmidt

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its counterpart-coarsening. In general, coarsening algorithms are mostly based on an explicitly given refinement history. In this work, we present a coarsening algorithm on adaptive red-green-blue meshes in two dimensions without explicitly knowing the refinement history. To this end, we examine the local structure of these meshes, find an easy-to-verify criterion to adaptively coarsen red-green-blue meshes, and prove that this criterion generates meshes with the desired properties. We present a MATLAB implementation built on the red-green-blue refinement routine of the ameshref-package (Funken and Schmidt 2018, 2019).



中文翻译:

自适应红绿蓝精制网格的粗化算法

自适应网格化是自适应有限元方法的基本组成部分。这包括局部细化和粗化网格。在这项工作中,我们关注二维的红绿蓝细化策略及其对应的粗化。通常,粗化算法主要基于明确给出的细化历史。在这项工作中,我们提出了在二维中自适应红绿蓝网格的粗化算法,而没有明确地知道细化历史。为此,我们检查了这些网格的局部结构,找到了易于验证的准则来自适应地粗化红绿蓝网格,并证明该准则生成了具有所需属性的网格。我们提出了一个基于ameshref的红绿蓝精炼例程的MATLAB实现-package(Funken和Schmidt 2018、2019)。

更新日期:2020-10-02
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