A superconvergent stencil-adaptive SBP-SAT finite difference scheme

Viktor Linders; Mark H. Carpenter; Jan Nordström

doi:10.1016/j.jcp.2024.112794

A superconvergent stencil-adaptive SBP-SAT finite difference scheme

Viktor Linders, Mark H. Carpenter, Jan Nordström

Research output: Contribution to journal › Article › peer-review

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).

Original language	English
Article number	112794
Journal	Journal of Computational Physics
Volume	501
DOIs	https://doi.org/10.1016/j.jcp.2024.112794
Publication status	Published - 2024 Mar 15

Subject classification (UKÄ)

Computational Mathematics

Free keywords

Adaptivity
Summation-by-parts
Superconvergence

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10.1016/j.jcp.2024.112794Licence: CC BY

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title = "A superconvergent stencil-adaptive SBP-SAT finite difference scheme",

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).",

keywords = "Adaptivity, Summation-by-parts, Superconvergence",

author = "Viktor Linders and Carpenter, {Mark H.} and Jan Nordstr{\"o}m",

note = "Funding Information: Jan Nordstr{\"o}m was supported by Vetenskapsr{\aa}det , Sweden [award no. 2021-05484 VR ] and University of Johannesburg . Publisher Copyright: {\textcopyright} 2024 The Author(s)",

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doi = "10.1016/j.jcp.2024.112794",

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AU - Linders, Viktor

AU - Carpenter, Mark H.

AU - Nordström, Jan

PY - 2024/3/15

Y1 - 2024/3/15

N2 - 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).

AB - 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).

KW - Adaptivity

KW - Summation-by-parts

KW - Superconvergence

U2 - 10.1016/j.jcp.2024.112794

DO - 10.1016/j.jcp.2024.112794

M3 - Article

AN - SCOPUS:85183586388

SN - 0021-9991

VL - 501

JO - Journal of Computational Physics

JF - Journal of Computational Physics

M1 - 112794

ER -

A superconvergent stencil-adaptive SBP-SAT finite difference scheme

Abstract

Subject classification (UKÄ)

Free keywords

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