The ‘recovered space’ advection scheme for lowest-order compatible finite element methods
•A new advection scheme is proposed for lowest-order compatible finite element spaces.•This advection scheme has second order numerical accuracy.•A proof of stability of the advection scheme is provided.•Properties of the advection scheme are investigated. We present a new compatible finite element...
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Published in | Journal of computational physics Vol. 390; pp. 342 - 358 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Cambridge
Elsevier Inc
01.08.2019
Elsevier Science Ltd |
Subjects | |
Online Access | Get full text |
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Summary: | •A new advection scheme is proposed for lowest-order compatible finite element spaces.•This advection scheme has second order numerical accuracy.•A proof of stability of the advection scheme is provided.•Properties of the advection scheme are investigated.
We present a new compatible finite element advection scheme for the compressible Euler equations. Unlike the discretisations described in Cotter and Kuzmin (2016) and Shipton et al. (2018), the discretisation uses the lowest-order family of compatible finite element spaces, but still retains second-order numerical accuracy. This scheme obtains this second-order accuracy by first ‘recovering’ the function in higher-order spaces, before using the discontinuous Galerkin advection schemes of Cotter and Kuzmin (2016). As well as describing the scheme, we also present its stability properties and a strategy for ensuring boundedness. We then demonstrate its properties through some numerical tests, before presenting its use within a model solving the compressible Euler equations. |
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ISSN: | 0021-9991 1090-2716 |
DOI: | 10.1016/j.jcp.2019.04.013 |