A structure-preserving Partitioned Finite Element Method for the 2D wave equation

Abstract

Discretizing open systems of conservation laws while preserving the power-balance at the discrete level can be achieved using a new Partitioned Finite Element Method (PFEM), where an integration by parts is performed only on a subset of the variables in the weak formulation. Moreover, since boundary control and observation appear naturally in this formulation, the method is suitable both for simulation and control of infinite-dimensional port-Hamiltonian systems (pHs). The method can be applied using FEM software, and comes along with worked-out test cases on the 2D wave equation in different geometries and coordinate systems.