This paper presents HDGlab, an open source MATLAB implementation of the hybridisable discontinuous Galerkin (HDG) method. The main goal is to provide a detailed description of both the HDG method for elliptic problems and its implementation available in HDGlab. Ultimately, this is expected to make this relatively new advanced discretisation method more accessible to the computational engineering community. HDGlab presents some features not available in other implementations of the HDG method that can be found in the free domain. First, it implements high-order polynomial shape functions up to degree nine, with both equally-spaced and Fekete nodal distributions. Second, it supports curved isoparametric simplicial elements in two and three dimensions. Third, it supports non-uniform degree polynomial approximations and it provides a flexible structure to devise degree adaptivity strategies. Finally, an interface with the open-source high-order mesh generator Gmsh is provided to facilitate its application to practical engineering problems.

中文翻译：

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HDGlab：MATLAB 中可混合不连续伽辽金方法的开源实现

本文介绍了 HDGlab，这是一种可混合不连续伽辽金 (HDG) 方法的开源 MATLAB 实现。主要目标是详细描述椭圆问题的 HDG 方法及其在 HDGlab 中可用的实现。最终，这有望使计算工程社区更容易使用这种相对较新的高级离散化方法。HDGlab 提供了一些在 HDG 方法的其他实现中不可用的功能，这些功能可以在免费域中找到。首先，它实现了高达 9 次的高阶多项式形状函数，具有等间距和 Fekete 节点分布。其次，它支持二维和三维的弯曲等参单纯元素。第三，它支持非均匀度多项式近似，并提供灵活的结构来设计度自适应策略。最后，提供了与开源高阶网格生成器 Gmsh 的接口，以促进其在实际工程问题中的应用。