Long-time behavior of a coupled heat-wave system using a structure-preserving finite element method

This work is a numerical investigation of the coupling between the heat and wave equations, recast as an interconnection of open port-Hamiltonian systems (pHs). A structure-preserving discretization suited to open pHs, based on a mixed finite element approximation space that includes boundary inputs and outputs, is shown to yield a semi-discrete power balance analogous to the continuous one. In the frequency domain, the semi-discretization captures the finite accumulation point in the spectrum, associated with highly-oscillatory eigenfunctions localized at the interconnection interface. In the time domain, the polynomial and logarithmic energy decays proved by Zhang and Zuazua (Arch. Rational Mech. Anal. 184, 2007) are recovered using a Crank-Nicolson scheme.

To cite this paper:
Haine Ghislain, Matignon Denis, Monteghetti Florian (2022) Long-time behavior of a coupled heat-wave system using a structure-preserving finite element method. Mathematical Reports; 24(1-2):1–29

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