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arXiv · 1811.06956

The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods

Thomas M. Bendall·Colin J. Cotter·Jemma Shipton
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Abstract

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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Thomas M. Bendall, Colin J. Cotter, Jemma Shipton. 2018-11-16. The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods. https://doi.org/10.1016/j.jcp.2019.04.013

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