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.

本文介绍了HDGlab，这是可混合的不连续Galerkin（HDG）方法的开源MATLAB实现。主要目的是提供有关椭圆问题的HDG方法及其在HDGlab中可用的实现的详细说明。最终，这有望使计算工程界更容易使用这种相对较新的高级离散化方法。HDGlab提供了在自由域中可以找到的HDG方法的其他实现中不可用的一些功能。首先，它实现了具有等距节点分布和Fekete节点分布的高达9级的高阶多项式形状函数。其次，它支持二维和三维的弯曲等参简单单元。第三，它支持非均匀度多项式逼近，并且为设计度适应性策略提供了灵活的结构。最后，提供了与开源高阶网格生成器Gmsh的接口，以方便将其应用于实际工程问题。