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