Studium der Eigenschwingungen eines zylindrischen Plasmas mit der Methode der finite Elemente (2008)
Finite Dimensional Approximation of Non-Linear Problems .1. Branches of Nonsingular Solutions (2006)
Numerical Modeling of Electromagnetic Casting Processes (2006)
Besson, O., Bourgeois, J., Chevalier, P. A., Rappaz, J., Touzani, R.
Consistency, Stability, a-Priori and a-Posteriori Errors for Nonlinear Problems (2006)
In an abstract framework similar to the one developed in Crouzeix-Rappaz [2], we present a formalism which makes precise the notions of consistency and stability for the finite element approximation...
On a 2-Dimensional Magnetohydrodynamic Problem .1. Modeling and Analysis (2006)
We consider a two-dimensional Magnetohydrodynamic system of equations describing the motion of a conducting fluid in which eddy currents flow. The mathematical model is derived and existence of...
Numerical Modeling of Induction-Heating for 2-Dimensional Geometries (2006)
Clain, S., Rappaz, J., Swierkosz, M., Touzani, R.
We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel...
Numerical Modeling of Induction-Heating of Long Workpieces (2006)
Chaboudez, C., Clain, S., Glardon, R., Rappaz, J., Swierkosz, M., Touzani, R.
We consider in this paper an induction heating process. A mathematical model is presented, together with numerical methods used in order to describe the magnetic field, as well as the temperature...
In an abstract framework we present a formalism which specifies the notions of consistency and stability of Petrov-Galerkin methods used to approximate nonlinear problems which are, in many practical...
Existence for a Stationary Model of Binary Alloy Solidification (2006)
Blanc, P., Gasser, L., Rappaz, J.
A proof of existence is given for a stationary model of alloy solidification. The system is composed of heat equation, solute equation and Navier-Stokes equations. In rite latter Carman-Kozeny...
Jacot, A., Swierkosz, M., Rappaz, J., Rappaz, M., Mari, D.
A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow...
Error estimates and adaptive finite elements for nonlinear diffusion-convection problems (2006)
Medina, J., Picasso, M., Rappaz, J.
A priori and a posteriori error estimates are presented for nonlinear diffusion-convection problems when using the classical Streamline Upwind Petrov-Galerkin (SUPG) scheme and numerical integration....
On a two-dimensional magnetohydrodynamic problem .2. Numerical analysis (2006)
We consider the numerical approximation of a two-dimensional magnetohydrodynamic problem by standard finite element techniques. The numerical analysis is made for the case of regular solutions of the...
Numerical modeling in induction heating for axisymmetric geometries (2006)
Chaboudez, C., Clain, S., Glardon, R., Mari, D., Rappaz, J., Swierkosz, M.
This paper deals with numerical simulation of induction heating for axisymmetric geometries. A mathematical model is presented, together with a numerical scheme based on the Finite Element Method. A...
On spectral pollution in the finite element approximation of thin elastic ''membrane'' shells (2006)
Rappaz, J., Hubert, J. S., Palencia, E. S., Vassiliev, D.
The bending terms in a shell are small with respect to membrane ones as the thickness tends to zero. Consequently, the membrane approximation gives a good description of vibration properties of a...
Ahmad, N., Combeau, H., Desbiolles, J. L., Jalanti, T., Lesoult, G., Rappaz, J., ...
Micro-macrosegregation calculations have been performed for a rectangular cavity containing either a Pb-48 wt pct Sn alloy or a Sn-5 wt pct Pb alloy. The numerical results calculated with a finite...
Conca, C., Duran, M., Rappaz, J.
The aim of this work is to derive rate of convergence estimates for the spectral approximation of a mathematical model which describes the vibrations of a solid-fluid type structure. First, we...
A quasi-static two-dimensional induction heating problem. I: Modelling and analysis (2006)
We consider a nonlinear elliptic-parabolic system modelling induction heating processes when a sinusoidal electromagnetic field is applied at the boundary of the inductor. The magnetic field...
A strongly nonlinear problem arising in glaciology (2006)
The computation of glacier movements leads to a system of nonlinear partial differential equations. The existence and uniqueness of a weak solution is established by using the calculus of variations....
Numerical simulation of free surface flows (2006)
Maronnier, V., Picasso, M., Rappaz, J.
A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining...
A quasi-static two-dimensional induction heating problem II. Numerical analysis (2006)
We consider a nonlinear elliptic-parabolic system which stems from the modelling of heat induction processes in which a sinusoidal electromagnetic field is applied at the boundary of the inductor....
We investigate the well-posedness of a phase-field model for the isothermal solidification of a binary alloy due to Warren-Boettinger [12]. Existence of weak solution as well as regularity and...
Numerical analysis of a non-singular boundary integral method: Part I. The circular case (2006)
In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we present here a method which consists in inverting, on a finite element space, a...
In this paper, a nonlinear problem corresponding to a simplified Oldroyd-B model without convective terms is considered. Assuming the domain to be a convex polygon, existence of a solution is proved...
Stability of time-splitting schemes for the Stokes problem with stabilized finite elements (2006)
The time-dependent Stokes problem is solved using continuous, piecewise linear finite elements and a classical stabilization procedure. Four order-one methods are proposed for the time...
Numerical analysis of a non-singular boundary integral method: Part II: The general case (2006)
In order to numerically solve the interior and the exterior Dirichlet problems for the Laplacian operator, we have presented in a previous paper a method which consists in inverting, on a finite...
Approximation of multi-scale elliptic problems using patches of finite elements (2006)
Glowinski, R., He, J. W., Rappaz, J., Wagner, J.
In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive...
The main goal of this article is to establish a priori and a posteriori error estimates for the numerical approximation of some non linear elliptic problems arising in glaciology. The stationary...
Numerical simulation of three-dimensional free surface flows (2006)
Maronnier, V., Picasso, M., Rappaz, J.
A numerical model is presented for the simulation of complex fluid flows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is...
A multi-domain method for solving numerically multi-scale elliptic problems (2006)
Glowinski, R., He, J. W., Rappaz, J., Wagner, J.
In this paper we present a family of iterative methods to solve numerically second order elliptic problems with multi-scale data using multiple levels of grids. These methods are based upon the...
Masserey, A., Rappaz, J., Rozsnyo, R., Touzani, R.
We present an extension of a 2D cartesian electromagnetic and thermal model to achieve the optimal control of an industrial induction heating system. The control variables are the frequency and the...
Optimal control of an induction heating process for thixoforming (2006)
Masserey, A., Rappaz, J., Rozsnyo, R., Touzani, R.
We investigate in this paper a numerical method to control the temperature of an induction heating process through electric current parameters such as frequency and current voltage imposed to the...
Numerical simulation of the motion of a two-dimensional glacier (2006)
Picasso, M., Rappaz, J., Reist, A., Funk, M., Blatter, H.
The motion of a two-dimensional glacier is considered. At each time step, given the shape of the glacier, ice is modelled as an incompressible non-Newtonian fluid and a non-linear elliptic problem...
Caboussat, A., Picasso, M., Rappaz, J.
A numerical model for the three-dimensional simulation of liquid-gas flows with free surfaces is presented. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain. In the...
Analysis of a one-dimensional free boundary flow problem (2006)
A one-dimensional free surface problem is considered. It consists in Burgers' equation with an additional diffusion term on a moving interval. The well-posedness of the problem is investigated and...
Duran, M., Ortega-Torres, E., Rappaz, J.
Our goal is to study the existence of weak solution for the stationary system of equations describing the solidification process of a binary alloy confined in a bounded regular domain in R-3 and...
Finite element approximation of multi-scale elliptic problems using patches of elements (2006)
Glowinski, R., He, J. W., Lozinski, A., Rappaz, J., Wagner, J.
In this paper we present a method for the numerical solution of elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating...
Numerical integration of the three-dimensional Green kernel for an electromagnetic problem (2006)
Masserey, A., Rappaz, J., Rozsnyo, R., Swierkosz, M.
In this paper, we present a method for the numerical integration of the three-dimensional Green kernel over two triangles. This method is compared with the results obtained by other algorithms. The...
Mathematical and numerical analysis of a three-dimensional fluid flow model in glaciology (2006)
The main goal of this article is to analyze a three-dimensional model for stress and velocity fields in grounded glaciers and ice sheets including the role of normal deviatoric stress gradients. This...
Simulation of solidification of alloys using the FEM code Modulef (2005)
Desbiolles, J. L., Rappaz, M., Droux, J. J., Rappaz, J., Fredriksson, H.
Modeling of solidification processes (2005)
Desbiolles, J. L., Droux, J. J., Hoadley, A. F. A., Rappaz, J., Rappaz, M., Gruber, R., ...
Ahmad, N., Combeau, H., Jalanti, T., Lesoult, G., Rappaz, J., ...
Ahmad, N., Combeau, H., Jalanti, T., Lesoult, G., Rappaz, J., ...
Jacot, A., Swierkosz, M., Rappaz, J., Rappaz, M., Mari, D.
A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow...
Jacot, A., Swierkosz, M., Rappaz, J., Rappaz, M., Mari, D.
A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow...
Jacot, A., Swierkosz, M., Rappaz, J., Rappaz, M., Mari, D.
A comprehensive micro-macroscopic model of the continuous hardening of 3d-axisymmetric steel components by induction heating has been developed. At the macroscopic scale, the Maxwell and heat flow...