an:02219978
Zbl 1086.65105
Arnold, Douglas N.; Boffi, Daniele; Falk, Richard S.
Quadrilateral \(H\)(div) finite elements
EN
SIAM J. Numer. Anal. 42, No. 6, 2429-2451 (2005).
00120541
2005
j
65N30 65N15
\(H\)(div) finite elements; Piola transformation; error estimates; quadrilateral Raviart-Thomas elements; numerical results
Finite elements in \(H\)(div) on quadrilaterals require that the Piola transformation is used when going from the reference element to the quadrilateral in the physical domain. For this reason the usual condition on the reproduction of polynomials is not sufficient for guaranteeing an approximation of order \(r+1\). Extra conditions are considered. New error estimates for quadrilateral Raviart-Thomas elements are also derived, and a new quadrilateral element with approximation of full order is proposed. The paper concludes with numerical results.
Dietrich Braess (Bochum)