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This paper presents a structure-preserving spatial discretization method fordistributed parameter port-Hamiltonian systems. The class of considered systemsare hyperbolic systems of two conservation laws in arbitrary spatial dimensionand geometries. For these systems, a partioned finite element method isderived, based on the integration by parts of one of the two conservation lawswritten in weak form. The nonlinear 1D Shallow Water Equation (SWE) is firstconsidered as a motivation example. Then the method is investigated on theexample of the nonlinear 2D SWE. Complete derivation of the reducedfinite-dimensional port-Hamiltonian system is provided and numericalexperiments are performed. Extensions to curvilinear (polar) coordinatesystems, space-varying coefficients and higher-order port-Hamiltonian systems(Euler-Bernoulli beam equation) are provided.

A Partitioned Finite Element Method for power-preserving discretization of open systems of conservation laws