Strictly Uniform Exponential Decay of the Mixed-FEM Discretization for the Wave Equation With Boundary Dissipation

Authors

David C. Del Rey Fernández, Luis A. Mora, Kirsten Morris

Abstract

Uniform preservation of stability in approximations of wave equations is a long-standing issue. In this letter, a one-dimensional wave equation with a partially reflective boundary is approximated using a first-order mixed finite element method. The multiplier method is used to prove that the approximated systems are exponentially stable with a decay rate independent of the mesh size. Upper bounds on the exponential decay are obtained in terms of the physical parameters.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2023
• Volume: 7
• Issue:
• Pages: 2155–2160
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2023.3284801

BibTeX

@article{Del_Rey_Fern_ndez_2023,
  title={{Strictly Uniform Exponential Decay of the Mixed-FEM Discretization for the Wave Equation With Boundary Dissipation}},
  volume={7},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2023.3284801},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Del Rey Fernández, David C. and Mora, Luis A. and Morris, Kirsten},
  year={2023},
  pages={2155--2160}
}

Download the bib file

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