RAPETTI , Francesca

International audience

International audience

International audience

International audience

In a recent JCP paper (by Y. Liu et al., vol. 336, p. 458, 2017) a higher order triangular spectral element method (T SEM) is proposed to address seismic wave field modeling. The main interest of this T SEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. This property results from the fact that,...

Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard {lowest order} continuous finite elements with discontinuous gradients. \hh{As a consequence,} the location of critical points of the poloidal flux, that are of paramount...

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Existing finite element implementations for the computation of free-boundary axisymmetric plasma equilibria approximate the unknown poloidal flux function by standard lowest order continuous finite elements with discontinuous gradients. As a consequence, the location of critical points of the poloidal flux, that are of paramount importance in...

We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped...

Low-order Whitney elements are widely used for electromagnetic field problems. Higher-order approximations are receiving increasing interest, but their definition remains unduly complex. In this paper we propose a new simple construction for Whitney p-elements of polynomial degree higher than one that use only degrees of freedom associated to...

We present a review in the construction of accurate and efficient multivariate polynomial approximations on elementary domains that are not Cartesian products of intervals, such as triangles and tetrahedra. After the generalities for high-order nodal interpolation of a function over an interval, we introduce collapsed coordinates and warped...

International audience

International audience

International audience

Explicit generators for high order ($r>1$) scalar and vector finite element spaces generally used in numerical electromagnetism are presented and classical degrees of freedom, the so-called moments, revisited. Properties of these generators on simplicial meshes are investigated and a general technique to restore duality between moments and...

We investigate the cubature points based triangular spectral element method and provide accuracy results for elliptic problems in non polygonal domains using various isoparametric mappings. The capabilities of the method are here again clearly confirmed.

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We review some concepts and basic features of high-order polynomial interpolation of fields in space. The interpolation, from weights, of Lagrange and Hermite types for physical fields, intended as differential forms, is analyzed on an interval.

We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to...

High order Whitney finite element spaces generally lack natural choices of bases but they do have spanning families. In these pages, we recall such a family on simplicial meshes and we prove theoretically its effectiveness. We also comment on some aspects of a new set of degrees of freedom, the so-called weights on the small simplices, to...