  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.
