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We consider the approximation properties of finite element spaces on quadrilateral meshes. The finite element spaces are constructed starting with a given finite dimensional space of functions on a square reference element , which is then transformed to a space of functions on each convex quadri-lateral element via a bilinear isomorphism of the square onto… (More)

We consider the approximation properties of quadrilateral finite element spaces of vector fields defined by the Piola transform, extending results previously obtained for scalar approximation. The finite element spaces are constructed starting with a given finite dimensional space of vector fields on a square reference element, which is then transformed to… (More)

In the approximation of linear elliptic operators in mixed form, it is well known that the so-called inf-sup and ellipticity in the kernel properties are sufficient (and, in a sense to be made precise, necessary) in order to have good approximation properties and optimal error bounds. One might think, in the spirit of Mercier-Osborn-Rappaz-Raviart and in… (More)

We study the approximation properties of a wide class of finite element differential forms on curvilinear cubic meshes in n dimensions. Specifically, we consider meshes in which each element is the image of a cubical reference element under a diffeomorphism, and finite element spaces in which the shape functions and degrees of freedom are obtained from the… (More)

This paper deals with the finite element approximation of evolution problems in mixed form. Following [8], we handle separately two types of problems. A model for the first case is the heat equation in mixed form, while the time dependent Stokes problem fits within the second one. For either case, we give sufficient conditions for a good approximation in… (More)

- Ivar Aavatsmark, Geir Terje Eigestad, Douglas N. Arnold, Richard S. Falk, Ragnar Winther, Timothy Barth +12 others

In this paper we prove the discrete compactness property for the edge element approximation of Maxwell's eigenpairs on general hp adaptive rectangular meshes. Hanging nodes, yielding 1-irregular meshes, are covered, and the order of the used elements can vary from one rectangle to the other, thus allowing for a real hp adaptivity. As a consequence of our… (More)