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Finite Element Methods for Maxwell's Equations$
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Peter Monk

Print publication date: 2003

Print ISBN-13: 9780198508885

Published to Oxford Scholarship Online: September 2007

DOI: 10.1093/acprof:oso/9780198508885.001.0001

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Finite Elements on Hexahedra

Finite Elements on Hexahedra

(p.155) 6 Finite Elements on Hexahedra
Finite Element Methods for Maxwell's Equations

Peter Monk

Oxford University Press

An alternative to the tetrahedral elements discussed in the previous chapter is to use finite elements based on cubes, or more generally, hexahedra. Hexahedral elements have been used in several important codes. This chapter concerns Nedelec’s family of edge and face elements on a hexahedral mesh with edges parallel to the coordinate axis. Conformance and unisolvence are proven, and h-error estimates are derived. The appropriate discrete de Rham diagram is shown to hold in this case, and boundary spaces are discussed briefly.

Keywords:   edge elements, face elements, interpolation error estimates, de Rham diagram, unisolvence

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