4.6 Article

ON PORT-HAMILTONIAN APPROXIMATION OF A NONLINEAR FLOW PROBLEM ON NETWORKS

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Article Mathematics, Applied

ON PORT-HAMILTONIAN APPROXIMATION OF A NONLINEAR FLOW PROBLEM ON NETWORKS

Bjoern Liljegren-Sailer et al.

Summary: This paper deals with the systematic development of structure-preserving approximations for a class of nonlinear partial differential equations on networks. The approach is guided by energy-based modeling concepts, such as the port-Hamiltonian formalism and the theory of Legendre transformation. The results show that under mild assumptions, local conservation of mass, an energy bound, and the inheritance of the port-Hamiltonian structure can be achieved. The method is not limited to conventional space discretization and can also handle complexity reduction of the nonlinearities by inexact integration.

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