Numerical approximation of a Bresse-Maxwell-Cattaneo system

Noelia Bazarra; José R. Fernández; Irea López; María Rodríguez-Damián; Noelia Bazarra; José R. Fernández; Irea López; María Rodríguez-Damián

doi:10.3934/era.2025172

Electronic Research Archive

2025, Volume 33, Issue 6: 3883-3900. doi: 10.3934/era.2025172

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Numerical approximation of a Bresse-Maxwell-Cattaneo system

1.
Departamento de Matemática Aplicada I, Universidade de Vigo, Escola de Enxeñería de Telecomunicación, Campus As Lagoas Marcosende s/n, Vigo 36310, Spain
2.
CINTECX, Departamento de Ingeniería Mecánica, Universidade de Vigo, Campus As Lagoas Marcosende s/n, Vigo 36310, Spain
3.
Departamento de Informática, Universidade de Vigo, Escola de Enxeñería Industrial, Vigo 36310, Spain

Received: 08 April 2025 Revised: 12 June 2025 Accepted: 17 June 2025 Published: 23 June 2025

In this paper, we analyze, from the numerical point of view, a new thermoelastic problem involving the so-called Bresse system. The heat conduction is modeled by using the Maxwell-Cattaneo law, which is of hyperbolic type. An existence and uniqueness result and an energy decay property are recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. First, we prove that the discrete solution is stable, and secondly, we provide an a priori error analysis. This allows us to conclude the linear convergence under suitable additional regularity on the continuous solution. Finally, numerical results are presented to demonstrate the convergence of the scheme and the behavior of the discrete energy.
- Bresse-Maxwell-Cattaneo system,
- hyperbolic heat conduction,
- finite elements,
- discrete stability,
- error estimates,
- numerical results
Citation: Noelia Bazarra, José R. Fernández, Irea López, María Rodríguez-Damián. Numerical approximation of a Bresse-Maxwell-Cattaneo system[J]. Electronic Research Archive, 2025, 33(6): 3883-3900. doi: 10.3934/era.2025172

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Abstract

In this paper, we analyze, from the numerical point of view, a new thermoelastic problem involving the so-called Bresse system. The heat conduction is modeled by using the Maxwell-Cattaneo law, which is of hyperbolic type. An existence and uniqueness result and an energy decay property are recalled. Then, fully discrete approximations are introduced by using the finite element method and the implicit Euler scheme. First, we prove that the discrete solution is stable, and secondly, we provide an a priori error analysis. This allows us to conclude the linear convergence under suitable additional regularity on the continuous solution. Finally, numerical results are presented to demonstrate the convergence of the scheme and the behavior of the discrete energy.

References

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