An Iterative Method for Solving Non-Linear Hydromagnetic Equations

We propose an iterative finite element method for solving non-linear hydromagnetic and steady Euler's equations. Some three-dimensional computational tests are given to confirm the convergence and the high efficiency of the method

Computing Beltrami Fields

International audienceFor solving the nonlinear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is solved by means of a mixed method. The last problem is a transport equation which is approximated using a streamline diffusion technique. Numerical three-dimensional experiments and results are given to illustrate the efficiency of the method

Inverted finite elements: a new method for solving elliptic problems in unbounded domains

In this paper, we propose a new numerical method for solving elliptic equations in unbounded regions of ${\mathbb{R}}^n$. The method is based on the mapping of a part of the domain into a bounded region. An appropriate family of weighted spaces is used for describing the growth or the decay of functions at large distances. After exposing the main ideas of the method, we analyse carefully its convergence. Some 3D computational results are displayed to demonstrate its efficiency and its high performance

A new mathematical formulation of the equations of perfect elasto-plasticity

International audienceA new mathematical formulation for the constitutive laws governing elastic perfectly plastic materials is proposed here. In particular, it is shown that the elastic strain rate and the plastic strain rate form an orthogonal decomposition with respect to the tangent cone and the normal cone of the yield domain. It is also shown that the stress rate can be seen as the projection on the tangent cone of the elastic stress tensor. This approach leads to a coherent mathematical formulation of the elasto-plastic laws and simplifies the resulting system for the associated flow evolution equations. The cases of one or two yield functions are treated in detail. The practical examples of the von Mises and Tresca yield criteria are worked out in detail to demonstrate the usefulness of the new formalism in applications

Some identities on weighted Sobolev spaces.

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Computing Beltrami Fields

International audienceFor solving the nonlinear equations governing force-free fields, an iterative methodology based on the splitting of the problem is described. On the basis of this splitting, three families of subproblems have to be solved numerically. The first problem consists to find a potential field. A mixed hybrid method is used to solve it. The second problem, which is a curl-div system, is solved by means of a mixed method. The last problem is a transport equation which is approximated using a streamline diffusion technique. Numerical three-dimensional experiments and results are given to illustrate the efficiency of the method

On the linear force-free fields in bounded and unbounded three-dimensional domains

Linear Force-free (or Beltrami) fields are three-components divergence-free fields solutions of the equation curlB = αB, where α is a real number. Such fields appear in many branches of physics like astrophysics, fluid mechanics, electromagnetics and plasma physics. In this paper, we deal with some related boundary value problems in multiply-connected bounded domains, in half-cylindrical domains and in exterior domains