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In this article, we consider the initial value problem which is obtained after a space discretization (with space step ) of the equations governing the solidification process of a multicomponent alloy. We propose a numerical scheme to solve numerically this initial value problem. We prove an error estimate which is not affected by the step size chosen in the space discretization. Consequently, our scheme provides global convergence without any stability condition between and the time step size...
In this article, we consider the initial value problem which is obtained
after a space discretization (with space step h)
of the equations governing the solidification process of
a multicomponent alloy.
We propose a numerical scheme to solve numerically this initial value
problem. We prove an error estimate which is not affected by
the step size h chosen in the space discretization. Consequently, our scheme
provides global convergence without any stability condition between h and
the time...
An iterative procedure for systems with matrices originalting from the domain decomposition technique is proposed. The procedure introduces one iteration parameter. The convergence and optimization of the method with respect to the parameter is investigated. The method is intended not as a preconditioner for the CG method but for the independent use.
We present in this paper a pressure correction scheme for the drift-flux model combining finite element and finite volume discretizations, which is shown to enjoy essential stability features of the continuous problem: the scheme is conservative, the unknowns are kept within their physical bounds and, in the homogeneous case (i.e. when the drift velocity vanishes), the discrete entropy of the system decreases; in addition, when using for the drift velocity a closure law which takes the form of...
We present in this paper a pressure correction scheme for the barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the continuous problem also hold for the discrete solution.
The stability proof is based on two independent results for general finite volume discretizations, both interesting for their own sake: the L2-stability of the discrete advection operator provided it...
In this paper, we construct a combined upwinding and mixed finite
element method for the numerical solution of a two-dimensional mean
field model of superconducting vortices. An advantage of our method
is that it works
for any unstructured regular triangulation. A simple convergence
analysis is given without resorting to the discrete maximum principle.
Numerical examples are also presented.
In this work, we address the problem of fluid-structure interaction (FSI) with moving structures that may come into contact. We propose a penalization contact algorithm implemented in an unfitted numerical framework designed to treat large displacements. In the proposed method, the fluid mesh is fixed and the structure meshes are superimposed to it without any constraint on the conformity. Thanks to the Extended Finite Element Method (XFEM), we can treat discontinuities of the fluid solution on...
A coupled finite/boundary element method to approximate the free vibration modes of an elastic structure containing an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of one of the most usual procedures in engineering practice: an added mass formulation, which is posed in terms of boundary integral equations. Piecewise linear continuous elements are used to discretize the solid displacements and the fluid-solid interface variables. Spectral...
A coupled finite/boundary element method to approximate the free
vibration modes of an elastic structure containing an incompressible
fluid is analyzed in this paper. The effect of the fluid is taken into
account by means of one of the most usual procedures in engineering
practice: an added mass formulation, which is posed in terms of
boundary integral equations. Piecewise linear continuous elements are
used to discretize the solid displacements and the fluid-solid
interface variables....
Currently displaying 301 –
320 of
1417