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Hexahedral H(div) and H(curl) finite elements*

Published online by Cambridge University Press:  10 May 2010

Richard S. Falk ,
Paolo Gatto  and
Peter Monk
Richard S. Falk
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854-8019, USA. falk@math.rutgers.edu
Paolo Gatto
Affiliation:
Inst. for Comp. Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, USA. gatto@ices.utexas.edu
Peter Monk
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA. monk@math.udel.edu
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Abstract

We study the approximation properties of some finite element subspaces ofH(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. Thiswork extends results previously obtained for quadrilateral H(div;Ω) finiteelements and for quadrilateral scalar finite element spaces. The finiteelement spaces we consider are constructed starting from a given finitedimensional space of vector fields on the reference cube, which is thentransformed to a space of vector fields on a hexahedron using the appropriatetransform (e.g., the Piola transform) associated to a trilinear isomorphism ofthe cube onto the hexahedron. After determining what vector fields are neededon the reference element to insure O(h) approximation in L 2(Ω) andin H(div;Ω) and H(curl;Ω) on the physical element, we study the properties ofthe resulting finite element spaces.

Keywords

Hexahedral finite element
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 45 , Issue 1 , January 2011 , pp. 115 - 143
Copyright
© EDP Sciences, SMAI, 2010

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