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Gibson, Andrew T.T. McRae, Colin J. Cotter, Lawrence Mitchell, David A. Ham 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (126 pages) 225 1 $aSpringerBriefs in Mathematics of Planet Earth, Weather, Climate, Oceans,$x2509-7326 311 08$a3-030-23956-X 327 $aPreface -- Geophysical Fluid Dynamics and Simulation -- Finite Element Methods for Geophysical Flows -- Firedrake -- Models in Two-Dimensions -- Models in Three-Dimensions -- References -- Index. 330 $aThis book introduces recently developed mixed finite element methods for large-scale geophysical flows that preserve essential numerical properties for accurate simulations. The methods are presented using standard models of atmospheric flows and are implemented using the Firedrake finite element library. Examples guide the reader through problem formulation, discretisation, and automated implementation. The so-called ?compatible? finite element methods possess key numerical properties which are crucial for real-world operational weather and climate prediction. The authors summarise the theory and practical implications of these methods for model problems, introducing the reader to the Firedrake package and providing open-source implementations for all the examples covered. Students and researchers with engineering, physics, mathematics, or computer science backgrounds will benefit from this book. 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