Pseudo-conforming polynomial finite elements on quadrilaterals

International audienceThe aim of this paper is to present a new class of finite elements on quadrilaterals where the approximation is polynomial on each element K. In the case of Lagrange finite elements, the degrees of freedom are the values at the vertices and in the case of mixed finite elements the degrees of freedom are the mean values of the fluxes on each side. The degres of freedom are the same as those of classical finite elements. However, in general, with this kind of finite elements,the resolution of second order elliptic problems leads to non conforming approximations. In the particular case when the finite elements are parallelograms, we can notice that our method is conform and coincides with the classical finite elements on structured meshes. First, a motivation for the study of the Pseudo-conforming polynomial finite elements method is given, and the convergence of the method established. Then, numerical results that confirm the error estimates, predicted by the theory, are presented

Pseudo-conforming Hdiv polynomial finite elements on quadrilaterals and hexahedra

The aim of this paper is to present a new class of mixed finite elements on quadrilaterals and hexahedra where the approximation is polynomial on each element K. The degrees of freedom are the same as those of classical mixed finite elements. However, in general, with this kind of finite elements, the resolution of second order elliptic problems leads to non conforming approximations. In the particular case when the finite elements are parallelograms or parallelepipeds, we can notice that our method is conform and coincides with the classical mixed finite elements on structured meshes. First, a motivation for the study of the Pseudo-conforming polynomial mixed finite elements method is given, and the convergence of the method established. Then, numerical results that confirm the error estimates, predicted by the theory, are presented.Le but de ce travail est de présenter une nouvelle classe d'éléments finis mixtes pour des maillages en quadrilatères et en hexaèdres pour lesquels l'approximation est polynômiale sur chaque élément K. Les degrés de liberté sont les même que ceux des éléments finis mixtes classiques. Cependant, avec ce nouveau type d'élément fini, la résolution de problèmes elliptiques du second ordre ne fournit pas, en général,une approximation conforme. Mais dans le cas particulier où les éléments sont des parallélogrammes ou des parallélépipèdes, on peut remarquer que notre méthode est conforme est coincide avec les éléments finis mixtes classiques sur des maillages structurés. Dans une première section on présente les motivations de cette étude. Dans la section suivante, on présente et étudie des 'eléments finis mixtes pseudo-conforme. Et dans la derni`re section on présente quelques tests numériques confirmant les résultats théoriques annoncés

Pseudo-Conforming Polynomial Lagrange Finite Elements on Quadrilaterals and Hexahedra

The aim of this paper is to develop a new class of finite elements on quadrilaterals and hexahedra. The degrees of freedom are the values at the vertices and the approximation is polynomial on each element K. In general, with this kind of finite elements, the resolution of second order elliptic problems leads to non-conform approximations. Degrees of freedom are the same than those of isoparametric finite elements. And, in the particular case when the finite elements are parallelotopes, our method is conform and coincides with the classical finite elements on structured meshes. The convergence of the method is analysed and the theory is confirmed by some numerical results

Pseudo Conforming Finite Elements on Quadrilaterals

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Pseudo-conform polynomial Lagrange finite elements on quadrilaterals and hexahedra.

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A robust variant of NXFEM for the interface problem

cited By (since 1996)0International audienceIn this note, we propose a modification of the NXFEM proposed in Hansbo and Hansbo (2002) [4] for the elliptic interface problem. It leads to a robust method not only with respect to the mesh-interface geometry, but also with respect to the diffusion parameters. Dans cette note, nous proposons une modification de NXFEM proposée dans Hansbo et Hansbo (2002) [4] pour le problème d'interface elliptique. Elle permet d'obtenir la robuste à la fois par rapport à la géometrie du maillage coupé par l'interface et par rapport aux paramètres de diffusion. © 2012