Continuous and hybrid finite elements for port-Hamiltonian systems

  • Brugnoli, Andrea (Technical University Berlin)
  • Rashad, Ramy (University of Twente)
  • Stramigioli, Stefano (University of Twente)

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A recent and promising paradigm to model coupled phenomena is the port-Hamiltonian frame- work. Numerical methods to discretize port-Hamiltonian systems need to retain their geometric structure in order to be successfully used for complex multiphysical applications. In this talk, a continuous Galerkin finite element exterior calculus formulation that is able to mimetically represent coupled conservation laws and their power balance is presented. The possibility of including open boundary conditions allows for modular composition of complex multi-physical systems whereas the exterior calculus formulation provides a coordinate-free treatment. The power balance characterizing the Stokes-Dirac structure is retrieved at the discrete level using the de Rham complex properties and symplectic Runge-Kutta integrators based on Gauss-Legendre collocation points. The proposed formulation is directly amenable to hybridization. The hybrid formulation is equivalent to the continuous Galerkin formulation and can be efficiently solved using a static condensation procedure in discrete time, leading to a much smaller system to be solved.