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Quadrilateral \(H\)(div) finite elements. (English) Zbl 1086.65105
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.

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65N15 Error bounds for boundary value problems involving PDEs
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