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