A novel approximation technique using Lagrange finite elements is proposed to solve magneto-dynamics problems involving discontinuous magnetic permeability and non-smooth interfaces. The algorithm is validated on benchmark problems and is used for kinematic studies of the Cadarache von Kármán Sodium 2 (VKS2) experimental fluid dynamo. 2011 Elsevier Inc. All rights reserved.

A synthesis of sliding mode control for a robot arm based on a robot model identified by neural networks is presented. The proposed structural feed-forward neural networks estimate the elements of the Lagrange-Euler mathematical model of robot, and they can be directly used for a synthesis of a model-based control system.

The 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 c...

We give error estimates for a mixed finite element approximation of the two-dimensional elliptic Monge-Ampère equation with the unknowns approximated by Lagrange finite elements of degree two. The variables in the formulation are the scalar variable and the Hessian matrix.

We study the quadratic Lagrange spectrum defined by Parkkonen and Paulin by considering the approximation by elements of the orbit of a given real quadratic irrational number for the action by homographies and anti-homographies of PSL2(Z) on R ∪ {∞}. Our approach is based on the theory of continued fractions.

Two types of stability boundaries exist for any planetary system consisting of one star and two planets. Lagrange stability requires that the planets remain bound to the star, conserves the ordering of the distance from the star, and limits the variations of orbital elements like semi-major axis and eccentricity. Hill stability only requires that the ordering of the planets remain constant; the...

We introduce noncommutative extensions of the Fourier transform of probability measures and its logarithm in the algebra A(S) of complex-valued functions on the free semigroup on two generators S = FS({z,w}). First, to given probability measures μ, ν whose all moments are finite, we associate states μ̂, ν̂ on the unital free *-bialgebra (B, ǫ,∆) on two self-adjoint generators X,X ′ and a projecti...

This article deals with solving partial differential equations with the finite element method on hybrid non-conforming hexahedral-tetrahedral meshes. By non-conforming, we mean that a quadrangular face of a hexahedron can be connected to two triangular faces of tetrahedra. We introduce a set of low-order continuous (C) finite element spaces defined on these meshes. They are built from standard ...

Systems subjected to holonomic constraints follow quite complicated dynamics that could not be described easily with Hamiltonian or Lagrangian dynamics. The influence of holonomic constraints in equations of motions is taken into account by using Lagrange multipliers. Finding the value of the Lagrange multipliers allows to compute the forces induced by the constraints and therefore, to integrat...