Volume 45, Number 1, January-February 2011
|Page(s)||115 - 143|
|Published online||10 May 2010|
Hexahedral H(div) and H(curl) finite elements*
Department of Mathematics, Rutgers University, Piscataway,
NJ 08854-8019, USA. firstname.lastname@example.org
2 Inst. for Comp. Engineering and Sciences, University of Texas at Austin, Austin, TX 78712, USA. email@example.com
3 Department of Mathematical Sciences, University of Delaware, Newark, DE 19716, USA. firstname.lastname@example.org
Revised: 18 November 2009
We study the approximation properties of some finite element subspaces of H(div;Ω) and H(curl;Ω) defined on hexahedral meshes in three dimensions. This work extends results previously obtained for quadrilateral H(div;Ω) finite elements and for quadrilateral scalar finite element spaces. The finite element spaces we consider are constructed starting from a given finite dimensional space of vector fields on the reference cube, which is then transformed to a space of vector fields on a hexahedron using the appropriate transform (e.g., the Piola transform) associated to a trilinear isomorphism of the cube onto the hexahedron. After determining what vector fields are needed on the reference element to insure O(h) approximation in L2(Ω) and in H(div;Ω) and H(curl;Ω) on the physical element, we study the properties of the resulting finite element spaces.
Mathematics Subject Classification: 65N30
Key words: Hexahedral finite element
© EDP Sciences, SMAI, 2010
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