We study a non linear functional which controls the area swept by a curve moving in the plane in the direction of curvature. In turn, this yields a priori estimates on solutions to a class of parabolic equations and of scalar viscous conservation laws. A further application provides an estimate on the “change of shape” of a BV solution to a scalar conservation law.

Streamribbon is used to visualize the rotation of the fluid flow. The rotation of flow is useful in fluid mechanics, engineering and geophysics. This paper introduces the construction technique of streamribbon using the streamline which is generated based on the law of mass conservation. The accuracy of constructed streamribbons is shown through two examples. Keywords—Mass conservation, streaml...

A dual mixed finite element method, for quasi–Newtonian fluid flow obeying to the power law, is constructed and analyzed in [8]. This mixed formulation possesses local (i.e., at element level) conservation properties (conservation of the momentum and the mass) as in the finite volume methods. We propose here an a posteriori error analysis for this mixed formulation.

An entropy solution u of a multi{dimensional scalar conservation law is not necessarily in BV , even if the conservation law is genuinely nonlinear. We show that u nevertheless has the structure of a BV {function in the sense that the shock location is codimension{one rectiiable. This result highlights the regularizing eeect of genuine non-linearity in a qualitative way; it is based on the loca...

Stochastic sandpiles self-organize to an absorbing-state critical point with scaling behavior different from directed percolation (DP) and characterized by the presence of an additional conservation law. This is usually called the C-DP or Manna universality class. There remains, however, an exception to this universality principle: a sandpile automaton introduced by Maslov and Zhang, which was ...

High-volume, multistage continuous production flow through a re-entrant factory is modeled through a conservation law for a continuous-density variable on a continuous-production line augmented by a state equation for the speed of the production along the production line. The resulting nonlinear, nonlocal hyperbolic conservation law allows fast and accurate simulations. Little’s law is built in...

M. A. Katsoulakis, G. Kossioris and Ch. Makridakis Abstract. We study discrete and semidiscrete relaxation schemes for multidimensional scalar conservation laws. We show convergence of the relaxation schemes to the entropy solution of the conservation law and derive error estimates that exhibit the precise interaction between the relaxation time and the space/time discretization parameters of t...

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...

This paper is devoted to the numerical analysis of the road traffic model proposed by Colombo and Goatin in [CG07]. The model involves a standard conservation law supplemented by a local unilateral constraint on the flux at the point x = 0 (modelling a road light, a toll gate, etc.). We first show that the problem can be interpreted in terms of the theory of conservation laws with discontinuous...

We show that relativistic dynamics can be approached without using conservation laws (conservation of momentum, of energy and of the centre of mass). Our approach avoids collisions that are not easy to teach without mnemonic aids. The derivations are based on the principle of relativity and on its direct consequence, the addition law of relativistic velocities.