Title:         Hexahedral H(div) and H(curl) finite elements
               

Authors:       Richard S. Falk, Paolo Gatto, and Peter Monk

Status:        ESAIM: Mathematical Modelling and Numerical 
               Analysis (M2AN), 45 (2011), pp. 115-143.

Abstract:      We study the approximation properties of some finite element
               subspaces of H(div) and H(curl) defined on hexahedral meshes in
               three dimensions.  This work extends results previously
               obtained for quadrilateral H(div) 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 L^2(\Omega) and in H(div) and H(curl) on the
               physical element, we study the properties of the resulting
               finite element spaces.

Keywords:      hexahedral finite element

Subj. class.:  65N30

URL:           http://www.math.rutgers.edu/~falk/papers/hexapprox-final.pdf