---
_id: '45954'
abstract:
- lang: eng
  text: "<jats:title>Abstract</jats:title>\r\n               <jats:p>$L^2$ norm error
    estimates of semi- and full discretizations of wave equations with dynamic boundary
    conditions, using bulk–surface finite elements and Runge–Kutta methods, are studied.
    The analysis rests on an abstract formulation and error estimates, via energy
    techniques, within this abstract setting. Four prototypical linear wave equations
    with dynamic boundary conditions are analysed, which fit into the abstract framework.
    For problems with velocity terms or with acoustic boundary conditions we prove
    surprising results: for such problems the spatial convergence order is shown to
    be less than 2. These can also be observed in the presented numerical experiments.</jats:p>"
author:
- first_name: David
  full_name: Hipp, David
  last_name: Hipp
- first_name: Balázs
  full_name: Kovács, Balázs
  last_name: Kovács
citation:
  ama: 'Hipp D, Kovács B. Finite element error analysis of wave equations with dynamic
    boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical Analysis</i>.
    2020;41(1):638-728. doi:<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>'
  apa: 'Hipp, D., &#38; Kovács, B. (2020). Finite element error analysis of wave equations
    with dynamic boundary conditions: <i>L</i>2 estimates. <i>IMA Journal of Numerical
    Analysis</i>, <i>41</i>(1), 638–728. <a href="https://doi.org/10.1093/imanum/drz073">https://doi.org/10.1093/imanum/drz073</a>'
  bibtex: '@article{Hipp_Kovács_2020, title={Finite element error analysis of wave
    equations with dynamic boundary conditions: <i>L</i>2 estimates}, volume={41},
    DOI={<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>},
    number={1}, journal={IMA Journal of Numerical Analysis}, publisher={Oxford University
    Press (OUP)}, author={Hipp, David and Kovács, Balázs}, year={2020}, pages={638–728}
    }'
  chicago: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave
    Equations with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal
    of Numerical Analysis</i> 41, no. 1 (2020): 638–728. <a href="https://doi.org/10.1093/imanum/drz073">https://doi.org/10.1093/imanum/drz073</a>.'
  ieee: 'D. Hipp and B. Kovács, “Finite element error analysis of wave equations with
    dynamic boundary conditions: <i>L</i>2 estimates,” <i>IMA Journal of Numerical
    Analysis</i>, vol. 41, no. 1, pp. 638–728, 2020, doi: <a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>.'
  mla: 'Hipp, David, and Balázs Kovács. “Finite Element Error Analysis of Wave Equations
    with Dynamic Boundary Conditions: <i>L</i>2 Estimates.” <i>IMA Journal of Numerical
    Analysis</i>, vol. 41, no. 1, Oxford University Press (OUP), 2020, pp. 638–728,
    doi:<a href="https://doi.org/10.1093/imanum/drz073">10.1093/imanum/drz073</a>.'
  short: D. Hipp, B. Kovács, IMA Journal of Numerical Analysis 41 (2020) 638–728.
date_created: 2023-07-10T11:42:43Z
date_updated: 2024-04-03T09:14:14Z
department:
- _id: '841'
doi: 10.1093/imanum/drz073
intvolume: '        41'
issue: '1'
keyword:
- Applied Mathematics
- Computational Mathematics
- General Mathematics
language:
- iso: eng
page: 638-728
publication: IMA Journal of Numerical Analysis
publication_identifier:
  issn:
  - 0272-4979
  - 1464-3642
publication_status: published
publisher: Oxford University Press (OUP)
status: public
title: 'Finite element error analysis of wave equations with dynamic boundary conditions:
  <i>L</i>2 estimates'
type: journal_article
user_id: '100441'
volume: 41
year: '2020'
...