A Partitioned Finite Element Method (PFEM) for power-preserving discretization of port-Hamiltonian systems (pHs) with polynomial nonlinearity

Abstract

The Partitioned Finite Element Method introduced in [IMA J. MCIControl and Information, 2021]. provides a structure-preserving discretization for the solution of systems of boundary controlled and observed Partial Differential Equations (PDEs), formulated as distributed-parameter port-Hamiltonian systems (pHs). In particular, the energy balance is preserved at the discrete level. This method, already well-developped for linear systems, is also suitable for nonlinear systems with polynomial nonlinearity, such as the 2D Shallow Water Equations, or the full von-Kármán plate equations.