 
Summary: COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING
Commun. Numer. Meth. Engng 2001; 17:805812 (DOI: 10.1002/cnm.450)
Finite element approximation on quadrilateral meshes
Douglas N. Arnold1;
, Daniele Bo ;2;
, Richard S. Falk3;§
and Lucia Gastaldi4;¶
1Department of Mathematics; Penn State University; University Park; PA 16802; U.S.A.
2Dipartimento di Matematica; UniversitÂa di Pavia; 27100 Pavia; Italy
3Department of Mathematics; Rutgers University; Piscataway; NJ 08854; U.S.A.
4Dipartmento di Matematica; UniversitÂa di Brescia; 25133 Brescia; Italy
SUMMARY
Quadrilateral ÿnite elements are generally constructed by starting from a given ÿnite dimensional space
of polynomials ^V on the unit reference square ^K. The elements of ^V are then transformed by using the
bilinear isomorphisms FK which map ^K to each convex quadrilateral element K. It has been recently
proven that a necessary and su cient condition for approximation of order r + 1 in L2
and r in H1
is
that ^V contains the space Qr of all polynomial functions of degree r separately in each variable. In this
paper several numerical experiments are presented which conÿrm the theory. The tests are taken from
