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Displaying 241 –
260 of
499
We introduce and analyze a numerical strategy to approximate effective coefficients in stochastic homogenization of discrete elliptic equations. In particular, we consider the simplest case possible: An elliptic equation on the d-dimensional lattice with independent and identically distributed conductivities on the associated edges. Recent results by Otto and the author quantify the error made by approximating the homogenized coefficient by the averaged energy of a regularized corrector (with...
We introduce and analyze a numerical strategy
to approximate effective coefficients in stochastic homogenization of discrete elliptic
equations. In particular, we consider the simplest case possible: An elliptic equation on
the d-dimensional lattice
with independent and identically distributed conductivities on the associated edges.
Recent results by Otto and the author quantify the error made by approximating
the homogenized coefficient by the averaged energy of a regularized
corrector (with...
In this paper the numerical solution of two dimensional fluid-structure interaction problem is addressed. The fluid motion is modelled by the incompressible unsteady Navier-Stokes equations. The spatial discretization by stabilized finite element method is used.
The motion of the computational domain is treated with the aid of Arbitrary Lagrangian Eulerian (ALE) method. The time-space problem is solved with the aid of multigrid method. The method is applied onto a problem of interaction of channel...
In this work, we consider the computation of the boundary conditions for the linearized
Euler–Poisson derived from the BGK kinetic model in the small mean free path regime.
Boundary layers are generated from the fact that the incoming kinetic flux might be far
from the thermodynamical equilibrium. In [2], the authors propose a method to compute
numerically the boundary conditions in the hydrodynamic limit relying on an analysis of
the boundary layers....
Numerical approximation of the flow of liquid crystals governed by the Ericksen-Leslie equations is considered. Care is taken to develop numerical schemes which inherit the Hamiltonian structure of these equations and associated stability properties. For a large class of material parameters compactness of the discrete solutions is established which guarantees convergence.
Numerical approximation of the flow of liquid crystals governed by
the Ericksen-Leslie equations is considered. Care is taken to
develop numerical schemes which inherit the Hamiltonian structure of
these equations and associated stability properties. For a large
class of material parameters compactness of the discrete solutions
is established which guarantees convergence.
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
A new set of nonlocal boundary conditions is proposed for the higher modes of the 3D inviscid primitive equations. Numerical schemes using the splitting-up method are proposed for these modes. Numerical simulations of the full nonlinear primitive equations are performed on a nested set of domains, and the results are discussed.
We consider functionals of a potential energy corresponding to . We are dealing with with . Various types of the subsoil of the plate are described by various types of the nonlinear term . The aim of the paper is to find a suitable computational algorithm.
The aim of this paper is to present a numerical approximation for quasilinear parabolic differential functional equations with initial boundary conditions of the Neumann type. The convergence result is proved for a difference scheme with the property that the difference operators approximating mixed derivatives depend on the local properties of the coefficients of the differential equation. A numerical example is given.
Using Burgers’ equation with mixed Neumann–Dirichlet boundary conditions, we highlight a problem that can arise in the numerical approximation of nonlinear dynamical systems on computers with a finite precision floating point number system. We describe the dynamical system generated by Burgers’ equation with mixed boundary conditions, summarize some of its properties and analyze the equilibrium states for finite dimensional dynamical systems that are generated by numerical approximations of this...
We first prove an abstract result for a class of nonlocal
problems using fixed point method. We apply this result to
equations revelant from plasma physic problems. These equations
contain terms like monotone or relative rearrangement of functions.
So, we start the approximation study by using finite element to
discretize this nonstandard quantities. We end the paper by giving
a numerical resolution of a model containing those terms.
We study numerically the semiclassical limit for the nonlinear
Schrödinger equation thanks to a modification of the Madelung
transform due to Grenier. This approach allows for the presence of
vacuum. Even if the mesh
size and the time step do not depend on the
Planck constant, we recover the position and current densities in the
semiclassical limit, with a numerical rate of convergence in
accordance with the theoretical
results, before shocks appear in the limiting Euler
equation. By using simple...
We study numerically the semiclassical limit for the nonlinear
Schrödinger equation thanks to a modification of the Madelung
transform due to Grenier. This approach allows for the presence of
vacuum. Even if the mesh
size and the time step do not depend on the
Planck constant, we recover the position and current densities in the
semiclassical limit, with a numerical rate of convergence in
accordance with the theoretical
results, before shocks appear in the limiting Euler
equation. By using simple...
Currently displaying 241 –
260 of
499