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

lymph: discontinuous poLYtopal methods for Multi-PHysics differential problems