We present the library lymph for the finite element numerical discretization of coupled multi-physics problems. lymph is a Matlab library for the discretization of partial differential equations based on high-order discontinuous Galerkin methods on polytopal grids (PolyDG) for spatial discretization coupled with suitable finite-difference time marching schemes. The objective of the paper is to introduce the library by describing it in terms of installation, input/output data, and code structure, highlighting - when necessary - key implementation aspects related to the method. A user guide, proceeding step-by-step in the implementation and solution of a Poisson problem, is also provided. In the last part of the paper, we show the results obtained for several differential problems, namely the Poisson problem, the heat equation, and the elastodynamics system. Through these examples, we show the convergence properties and highlight some of the main features of the proposed method, i.e. geometric flexibility, high-order accuracy, and robustness with respect to heterogeneous physical parameters.

翻译：我们介绍了用于耦合多物理场问题有限元数值离散化的淋巴库。淋巴是一个基于高阶不连续伽辽金方法在多变体网格上进行空间离散化，并结合合适有限差分时间推进格式的偏微分方程离散化Matlab库。本文旨在通过描述该库的安装、输入/输出数据和代码结构来介绍该库，并在必要时强调与方法相关的关键实现方面。我们还提供了一份用户指南，逐步指导泊松问题的实现和求解过程。在文章的最后部分，我们展示了针对几个微分问题（即泊松问题、热方程和弹性动力学系统）所获得的结果。通过这些例子，我们展示了收敛性质，并强调了所提出方法的一些主要特点，即几何灵活性、高阶精度以及对异质物理参数的鲁棒性。