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Journal Articles Mathematical Reports Year : 2022

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

Abstract

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.
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Dates and versions

hal-03722880 , version 1 (13-07-2022)

Identifiers

  • HAL Id : hal-03722880 , version 1
  • OATAO : 29099

Cite

Ghislain Haine, Denis Matignon, Florian Monteghetti. Long-time behavior of a coupled heat-wave system using a structure-preserving finite element method. Mathematical Reports, 2022, 22 (1-2), pp.187-215. ⟨hal-03722880⟩
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