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On Helmholtz decompositions and their generalizations—An overview

✍ Scribed by W. Sprössig

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
159 KB
Volume
33
Category
Article
ISSN
0170-4214

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✦ Synopsis

Abstract

Helmholtz' theorem initiates a remarkable development in the theory of projection methods that are adapted to the numerical solution of equations in fluid dynamics and elasticity. There is a dense connection with Hodge‐de Rham decompositions of smooth 1‐forms. We give an overview of this type of decompositions and discuss their applications to vector, quaternionic and Clifford‐valued boundary value problems in the corresponding Hilbert–Sobolev spaces. Copyright © 2009 John Wiley & Sons, Ltd.

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