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Displaying 101 –
120 of
487
The authors study problems of existence and uniqueness of solutions of various variational formulations of the coupled problem of dynamical thermoelasticity and of the convergence of approximate solutions of these problems.
First, the semidiscrete approximate solutions is defined, which is obtained by time discretization of the original variational problem by Euler’s backward formula. Under certain smoothness assumptions on the date authors prove existence and uniqueness of the solution and establish...
We study the gradient flow for the total variation functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow, and establish well-posedness of the problem by the energy method. The main idea of our approach is to exploit the relationship between the regularized gradient flow (characterized by a small positive parameter , and the minimal surface flow [21] and the prescribed mean curvature flow [16]. Since our...
We study the gradient flow for the total variation
functional, which arises in image processing and geometric applications. We propose a variational inequality weak formulation for the gradient flow,
and establish well-posedness of the problem by the energy method.
The main idea of our approach is to exploit the relationship between
the regularized gradient flow (characterized by a small positive parameter
ε, see (1.7)) and the minimal surface flow [21]
and the prescribed mean curvature flow [16].
Since...
We discuss the issues of implementation of a higher order discontinuous Galerkin (DG)
scheme for aerodynamics computations. In recent years a DG method has intensively been
studied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has been
designed for numerical solution of the 3-D Euler and Navier-Stokes equations. Our
discussion is mainly based on the results of the DG study conducted in TsAGI in
collaboration with the NUMECA...
We have developed a multiphase flow code that has been applied to study the behavior of non-aqueous phase liquids (NAPL) in the subsurface. We describe model formulation, discretization, and use the model for numerical investigation of sensitivity of the NAPL plume with respect to capillary parameters of the soil. In this paper the soil is assumed to be spatially homogeneous. A 2-D reference problem has been chosen and has been recomputed repeatedly with modified parameters of the Brooks–Corey capillary...
We illustrate how some interesting new variational principles can be
used for the numerical approximation of solutions to certain (possibly
degenerate) parabolic partial differential equations. One remarkable
feature of the algorithms presented here is that derivatives do not
enter into the variational principles, so, for example, discontinuous
approximations may be used for approximating the heat equation. We
present formulae for computing a Wasserstein metric which enters
into the variational...
In the reliability theory, the availability of a component, characterized by non constant failure and repair rates, is obtained, at a given time, thanks to the computation of the marginal distributions of a semi-Markov process. These measures are shown to satisfy classical transport equations, the approximation of which can be done thanks to a finite volume method. Within a uniqueness result for the continuous solution, the convergence of the numerical scheme is then proven in the weak measure sense,...
In the reliability theory, the availability of
a component, characterized by non constant failure and repair rates,
is obtained, at a given time, thanks to the computation of the marginal distributions of a
semi-Markov process. These measures are shown to satisfy classical
transport equations, the approximation of which can be done
thanks to a finite volume method.
Within a uniqueness result for the continuous solution,
the convergence of the numerical scheme is
then proven in the weak measure...
The paper deals with an initial problem of a parabolic variational inequality whichcontains a nonlinear elliptic form having a potential , which is twice -differentiable at arbitrary . This property of makes it possible to prove convergence of an approximate solution defined by a linearized scheme which is fully discretized - in space by the finite elements method and in time by a one-step finite-difference method. Strong convergence of the approximate solution is proved without any regularity...
Computers are becoming sufficiently powerful to permit to numerically solve problems such as the wave equation with high-order methods. In this article we will consider Lagrange finite elementsof order k and show how it is possible to automatically generate the mass and stiffness matrices of any order with the help of symbolic computation software. We compare two high-order time discretizations: an explicit one using a Taylor expansion in time (a Cauchy-Kowalewski procedure) and an implicit Runge-Kutta...
The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the...
We consider space semi-discretizations of the 1-d wave equation in a bounded
interval with homogeneous Dirichlet boundary conditions. We analyze the problem
of boundary observability, i.e., the problem of whether the total energy of
solutions can be estimated uniformly in terms of the energy concentrated on the
boundary as the net-spacing h → 0. We prove that, due to the spurious modes
that the numerical scheme introduces at high frequencies, there is no such a
uniform bound. We prove however a...
Currently displaying 101 –
120 of
487