The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods
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.
Keywords
Cite
@article{arxiv.1811.06956,
title = {The Recovered Space Advection Scheme for Lowest-Order Compatible Finite Element Methods},
author = {Thomas M. Bendall and Colin J. Cotter and Jemma Shipton},
journal= {arXiv preprint arXiv:1811.06956},
year = {2019}
}