Authors

Robert C. Kirby, Thinh Tri Kieu

Abstract

We apply mixed finite element approximations to the first-order form of the acoustic wave equation. The semidiscrete method exactly conserves the system energy. A fully discrete method employing the symplectic Euler time method in time exactly conserves a positive-definite pertubed energy functional that is equivalent to the actual energy under a CFL condition. In addition to proving optimal-order \( \)L^\infty (L^2)\( \) L ∞ ( L 2 ) estimates, we also develop a bootstrap technique that allows us to derive stability and error bounds for the time derivatives and divergence of the vector variable beyond the standard under some additional regularity assumptions.

Keywords

65M60; 65M12; 65P10

Citation

  • Journal: Numerische Mathematik
  • Year: 2015
  • Volume: 130
  • Issue: 2
  • Pages: 257–291
  • Publisher: Springer Science and Business Media LLC
  • DOI: 10.1007/s00211-014-0667-4

BibTeX

@article{Kirby_2014,
  title={{Symplectic-mixed finite element approximation of linear acoustic wave equations}},
  volume={130},
  ISSN={0945-3245},
  DOI={10.1007/s00211-014-0667-4},
  number={2},
  journal={Numerische Mathematik},
  publisher={Springer Science and Business Media LLC},
  author={Kirby, Robert C. and Kieu, Thinh Tri},
  year={2014},
  pages={257--291}
}

Download the bib file

References

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