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- Douglas N. Arnold, Daniele Boffi, Richard S. Falk
- SIAM J. Numerical Analysis
- 2005

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)

- Douglas N. Arnold, Daniele Boffi, Richard S. Falk
- Math. Comput.
- 2002

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 quadrilateral element via a bilinear isomorphism of the square onto… (More)

- Daniele Boffi
- Numerische Mathematik
- 2000

- Daniele Boffi, Franco Brezzi, Lucia Gastaldi
- Math. Comput.
- 2000

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)

- Daniele Boffi, Matteo Conforti, Lucia Gastaldi
- Numerische Mathematik
- 2006

The immersed boundary method is both a mathematical formulation and a numerical method. In its continuous version it is a fully non-linearly coupled formulation for the study of fluid structure interactions. As it is common in these cases, many numerical methods have been introduced to reduce the difficulties related to the non-linear coupling between the… (More)

The immersed boundary (IB) method is both a mathematical formulation and a numerical method for fluid-structure interaction problems, where immersed incompressible viscoelastic bodies or boundaries interact with an incompressible fluid. Previous formulations of the IB method were not able to treat appropriately thick materials modeled by hyper-elastic… (More)

- Daniele Boffi, Martin Costabel, Monique Dauge, Leszek F. Demkowicz
- SIAM J. Numerical Analysis
- 2006

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)

- Daniele Boffi, Nicola Cavallini, Francesca Gardini, Lucia Gastaldi
- J. Sci. Comput.
- 2012