This contribution introduces the idea of refinement patterns for the generation of optimal meshes in the context of the Finite Element Method. The main idea is to generate a library of possible patterns on which elements can be refined and use this library to inform an h adaptive code on how to handle complex refinements in regions of interest. There are no restrictions on the type of elements that can be refined, and the patterns can be generated for any element type. The main advantage of this approach is that it allows for the generation of optimal meshes in a systematic way where, even if a certain pattern is not available, it can easily be included through a simple text file with nodes and sub-elements. The contribution presents a detailed methodology for incorporating refinement patterns into h adaptive Finite Element Method codes and demonstrates the effectiveness of the approach through mesh refinement of problems with complex geometries.

翻译：本文提出了在有限元法中利用细化模式生成最优网格的思想。其主要思想是构建一个包含所有可能细化模式的库，元素可基于该库进行细化，并通过该库指导h自适应代码处理感兴趣区域中的复杂细化问题。该方法对可细化的元素类型无限制，且针对任意元素类型均可生成细化模式。该方案的主要优势在于能够系统性地生成最优网格：即使某个特定模式不可用，也只需通过包含节点和子元素的简单文本文件即可轻松添加。本文详细阐述了将细化模式融入h自适应有限元法代码的方法论，并通过复杂几何问题的网格细化验证了该方法的有效性。