Abstract
In this chapter, we introduce some basic concepts for discretisation of geophysical fluid models, motivated by the compatible finite element framework. We begin by defining compatible finite element spaces in two dimensions, before using them to describe a compatible finite element discretisation of the shallow water equations. Then, we’ll extend these ideas to three dimensions and discuss the spaces that are used to implement three dimensional geophysical flows with advected temperature.
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© 2019 The Author(s), under exclusive licence to Springer Nature Switzerland AG
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Gibson, T.H., McRae, A.T.T., Cotter, C.J., Mitchell, L., Ham, D.A. (2019). Finite Element Methods for Geophysical Flows. In: Compatible Finite Element Methods for Geophysical Flows. Mathematics of Planet Earth(). Springer, Cham. https://doi.org/10.1007/978-3-030-23957-2_2
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DOI: https://doi.org/10.1007/978-3-030-23957-2_2
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Publisher Name: Springer, Cham
Print ISBN: 978-3-030-23956-5
Online ISBN: 978-3-030-23957-2
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