Abstract This paper deals with the efficient implementation of various adaptive mesh refinements in two dimensions in Matlab. We give insights into different adaptive mesh refinement strategies allowing triangular and quadrilateral grids with and without hanging nodes. Throughout, the focus is on an efficient implementation by utilization of reasonable data structure, use of Matlab built-in functions and vectorization. This paper shows the transition from theory to implementation in a clear way and thus is meant to serve educational purposes of how to implement a method while keeping the code as short as possible – an implementation of an efficient adaptive mesh refinement is possible within 71 lines of Matlab. Numerical experiments underline the efficiency of the code and show the flexible deployment in different contexts where adaptive mesh refinement is in use. Our implementation is accessible and easy-to-understand and thus considered to be a valuable tool in research and education.

中文翻译：

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2D 中的自适应网格细化——Matlab 中的有效实现

摘要 本文讨论了如何在 Matlab 中有效地实现二维中的各种自适应网格细化。我们深入了解不同的自适应网格细化策略，允许带有和不带有悬挂节点的三角形和四边形网格。在整个过程中，重点是通过利用合理的数据结构、使用 Matlab 内置函数和矢量化来有效实现。这篇论文以清晰的方式展示了从理论到实现的转变，因此旨在服务于如何实现方法的教育目的，同时保持代码尽可能短——在 71 行代码中可以实现高效的自适应网格细化MATLAB。数值实验强调了代码的效率，并展示了在使用自适应网格细化的不同环境中的灵活部署。我们的实施易于访问且易于理解，因此被认为是研究和教育中的宝贵工具。