The Wave Equation as a Port-Hamiltonian System, and a Finite Dimensional Approximation
نویسنده
چکیده
The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of different geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a finite-dimensional portHamiltonian system, which also preserves the conservation laws.
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