We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit tim...

In this paper, we introduce an iterative scheme by viscosity approximation method for obtaining a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. We obtain a strong convergence which improves and extends S. Tak...

We study the linear response of living systems, which break and recombine randomly The mean field approximation gives an analytical solution for the time evolution of the response As an example, the viscosity of living polymers is computed New scaling laws for viscosity are found in the case of very short lifetimes The laws do not depend in an obvious

The eddy viscosity is the tensor in the equation that governs the transport of the large-scale (modulational) perturbations of small-scale stationary flows. As an approximation to eddy viscosity the effective tensor, that arises in the limit as the ratio between the scales ε → 0, can be considered. We are interested here in the accuracy of this approximation. We present results of computational...

In this paper we introduce a viscosity relaxed-extragradient method for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping in a real Hilbert space H . The viscosity relaxed-extragradient method is based on two methods: extragradientlike approximation method and ...

We consider the spectral approximation of a conservation law in the limit of small or vanishing viscosities. In this regime, the continuous solution of the problem is known to develop sharp spatial and temporal gradients referred to as shocks. Also, the standard Fourier–Galerkin solution is known to break down if the mesh parameter is larger than the shock width. In this paper we propose a new ...

The velocity, shear-rate, variable viscosity, and variable power-law index profiles are calculated for non-Newtonian fluids using the finite difference method. The calculations are carried out for an actual viscosity function obtained by a cilrve fit through measured data and for the corresponding power law model, the simplest and most often used form for non­ Newtonian viscosity function appro...

In this paper we prove that solutions of the 2D Euler equations in vorticity formulation obtained via vanishing viscosity approximation are renormalized.

Rosenau Phys. Rev. A, 40 (1989), pp. 7193-6] has recently proposed a regularized version of the Chapman-Enskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at law wave-numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the behavi...

ROSENAO [R] has recently proposed a regularized version of the ChapmanEnskog expansion of hydrodynamics. This regularized expansion resembles the usual Navier-Stokes viscosity terms at low wave numbers, but unlike the latter, it has the advantage of being a bounded macroscopic approximation to the linearized collision operator. In this paper we study the behavior of the Rosenau regularization o...