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

Mathematics and Applied Mathematics

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 - 15 Mar 2024

Keywords

Adaptivity
Summation-by-parts
Superconvergence

ASJC Scopus subject areas

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2024.112794

Cite this

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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",

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AU - Carpenter, Mark H.

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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

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DO - 10.1016/j.jcp.2024.112794

M3 - Article

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A superconvergent stencil-adaptive SBP-SAT finite difference scheme

Abstract

Keywords

ASJC Scopus subject areas

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