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A superconvergent stencil-adaptive SBP-SAT finite difference scheme

Linders, Viktor LU ; Carpenter, Mark H. and Nordström, Jan (2024) In Journal of Computational Physics 501.
Abstract

A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. As proof of concept, applied to the linear advection equation, it has a convergence rate O(Δx4) in contrast to a conventional scheme, which converges at a rate O(Δx3).

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author
; and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Adaptivity, Summation-by-parts, Superconvergence
in
Journal of Computational Physics
volume
501
article number
112794
publisher
Academic Press
external identifiers
  • scopus:85183586388
ISSN
0021-9991
DOI
10.1016/j.jcp.2024.112794
language
English
LU publication?
yes
additional info
Funding Information: Jan Nordström was supported by Vetenskapsrådet , Sweden [award no. 2021-05484 VR ] and University of Johannesburg . Publisher Copyright: © 2024 The Author(s)
id
71edd30d-c14a-462f-b2fe-a81479da701c
date added to LUP
2024-02-09 07:56:52
date last changed
2025-10-14 12:57:41
@article{71edd30d-c14a-462f-b2fe-a81479da701c,
  abstract     = {{<p>A stencil-adaptive SBP-SAT finite difference scheme is shown to display superconvergent behavior. As proof of concept, applied to the linear advection equation, it has a convergence rate O(Δx<sup>4</sup>) in contrast to a conventional scheme, which converges at a rate O(Δx<sup>3</sup>).</p>}},
  author       = {{Linders, Viktor and Carpenter, Mark H. and Nordström, Jan}},
  issn         = {{0021-9991}},
  keywords     = {{Adaptivity; Summation-by-parts; Superconvergence}},
  language     = {{eng}},
  month        = {{03}},
  publisher    = {{Academic Press}},
  series       = {{Journal of Computational Physics}},
  title        = {{A superconvergent stencil-adaptive SBP-SAT finite difference scheme}},
  url          = {{http://dx.doi.org/10.1016/j.jcp.2024.112794}},
  doi          = {{10.1016/j.jcp.2024.112794}},
  volume       = {{501}},
  year         = {{2024}},
}