Estimates Near Discontinuities for Some Difference Schemes.
Estimates of deviations from exact solutions of initial-boundary value problem for the heat equation
The paper is concerned with deriving functionals that give upper bounds of the difference between the exact solution of the initial-boundary value problem for the heat equation and any admissible function from the functional class naturally associated with this problem. These bounds are given by nonegative functionals called deviation majorants, which vanish only if the function and exact solution coincide. The deviation majorants pose a new type of a posteriori estimates that can be used in numerical...
Estimation of a temporally and spatially varying diffusion coefficinet in a parabolic system by an augmented Lagrangian technique.
Estimation of discontinuous parameters in general nonautonomous parabolic systems
Estimation of the conductivity in the one-phase Stefan problem : numerical results
Étude numérique des oscillations des systèmes semi-linéaires
Étude numérique des pôles de résonance associés à la diffraction d'ondes acoustiques et élastiques par un obstacle en dimension 2
Euler characteristic Galerkin scheme with recovery
Evolution of fluid-fluid interface in porous media as the model of gas-oil fields.
Exact, approximate solutions and error bounds for coupled implicit systems of partial differential equations.
Exact boundary controllability of Galerkin's approximations of Navier-Stokes equations
Existence and Approximation of Solutions of Non-Linear Elliptic Equations.
Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation
We consider the damped semilinear viscoelastic wave equation with nonlocal boundary dissipation. The existence of global solutions is proved by means of the Faedo-Galerkin method and the uniform decay rate of the energy is obtained by following the perturbed energy method provided that the kernel of the memory decays exponentially.
Existence and uniqueness of generalized solutions to a telegraph equation with an integral boundary condition via Galerkin's method.
Existence of solution a of nonlinear degenerate systems of parabolic variational inequalities
Existence of solutions to nonlinear advection-diffusion equation applied to Burgers' equation using Sinc methods
This paper has two objectives. First, we prove the existence of solutions to the general advection-diffusion equation subject to a reasonably smooth initial condition. We investigate the behavior of the solution of these problems for large values of time. Secondly, a numerical scheme using the Sinc-Galerkin method is developed to approximate the solution of a simple model of turbulence, which is a special case of the advection-diffusion equation, known as Burgers' equation. The approximate solution...
Existenzsätze mit der Linienmethode für Parabolische Probleme und periodische Lösungen von ut = f(t,x,u,ux,uxx).
Experimental comparison of traffic flow models on traffic data
Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model by Daganzo's...
Explicit Difference Approximations of Du Fort-Frankel Type of the One-Dimensional Diffusion Equation.
Explicit difference schemes for nonlinear differential functional parabolic equations with time dependent coefficients-convergence analysis
We study the initial-value problem for parabolic equations with time dependent coefficients and with nonlinear and nonlocal right-hand sides. Nonlocal terms appear in the unknown function and its gradient. We analyze convergence of explicit finite difference schemes by means of discrete fundamental solutions.