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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 having mixed boundary conditions. (c) 2005 Elsevier Ltd. All ...
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 extended to three dimensional situations. The mathematical ...
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 motion of a glacier is given by a non-Newtonian fluid flow mo ...
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 terminals of the inductor. We seek a sinusoidal voltage func ...
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 power. We explain how to derive the discrete optimal contr ...
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 introduction of a Lagrange multiplier to enforce the continuit ...
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 has to be solved to obtain the horizontal velocity field. T ...
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 corrections to the solution in patches whose discretizations ...
We consider an anisotropic phase-field model for the isothermal solidification of a binary alloy due to Warren-Boettinger (Acta. Metall. Mater. 1995; 43(2):689)., Existence of weak solutions is established under a certain convexity condition on the strongl ...
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 element space, a non-singular integral operator for circular ...
