Title: Finite element approximation on quadrilateral meshes
Authors: Douglas N. Arnold, Daniele Boffi, Richard S. Falk, and Lucia
Gastaldi
Source: Comm. Numer. Methods Engrg., 17(11):805-812, 2001.
Abstract: Quadrilateral finite elements are generally constructed by
starting from a given finite dimensional space of polynomials V^
on the unit reference square K^. The elements of V^ are then
transformed by using the bilinear isomorphisms F_K which map K^ to
each convex quadrilateral element K. It has been recently proven
that a necessary and sufficient condition for approximation of
order r+1 in L^2 and r in H^1 is that V^ contains the space Q_r of
all polynomial functions of degree r separately in each
variable. In this paper several numerical experiments are
presented which confirm the theory. The tests are taken from
various examples of applications: the Laplace operator, the Stokes
problem and an eigenvalue problem arising in fluid-structure
interaction modeling.
Keywords: quadrilateral, finite element, approximation,
serendipity, mixed finite element
URL: http://www.math.rutgers.edu/~falk/papers/quadmeshes.pdf