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Compatible Finite Element Methods for Geophysical Flows

Part of the Mathematics of Planet Earth Book Series

DOI: 10.1007/978-3-030-23957-2

ISBN: 978-3-030-23956-5

Publisher: Springer International Publishing - Springer Journals

Aug 27, 2019

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Chapter 1Geophysical Fluid Dynamics and Simulation

Gibson, Thomas H.; McRae, Andrew T. T.; Cotter, Colin J.; Mitchell, Lawrence; Ham, David A.

Pages: 1 –16

[In this chapter we describe various models for the atmosphere; they will be discretised in the rest of the book. We start by considering models with the fewest approximations and work our way down to simplified models.]
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Chapter 2Finite Element Methods for Geophysical Flows

Gibson, Thomas H.; McRae, Andrew T. T.; Cotter, Colin J.; Mitchell, Lawrence; Ham, David A.

Pages: 17 –38

[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...
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Chapter 3Firedrake

Gibson, Thomas H.; McRae, Andrew T. T.; Cotter, Colin J.; Mitchell, Lawrence; Ham, David A.

Pages: 39 –54

[The Firedrake project is an automated system for solving variational problems using the finite element method (Rathgeber et al., 2016). “Automated” in this context means that the user specifies the finite element problem symbolically using high level code that reflects the mathematical...
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Chapter 4Models in Two-Dimensions

Gibson, Thomas H.; McRae, Andrew T. T.; Cotter, Colin J.; Mitchell, Lawrence; Ham, David A.

Pages: 55 –74

[In this chapter we describe how to implement geophysical fluid dynamics models in Firedrake, focusing on two-dimensional models. The chapter is formed from code examples which highlight relevant aspects of the Firedrake modelling system. In particular, the definition and construction of...
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Chapter 5Models in Three-Dimensions

Gibson, Thomas H.; McRae, Andrew T. T.; Cotter, Colin J.; Mitchell, Lawrence; Ham, David A.

Pages: 75 –108

[As we move from two dimensional models, such as the shallow water equations discussed in the last chapter, to three dimensional models, the problem of efficient parallel iterative algorithms for implicit linear systems becomes an urgent priority. In this chapter we discuss some situations where...

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