A flux conserving meshfree method for conservation laws

A Nonlinear Flux Split Method for Hyperbolic Conservation Laws

A Wave Propagation Method for Conservation Laws and Balance Laws with Spatially Varying Flux Functions

We study a general approach to solving conservation laws of the form qt+f(q, x)x = 0, where the flux function f(q, x) has explicit spatial variation. Finite-volume methods are used in which the flux is discretized spatially, giving a function fi(q) over the ith grid cell and leading to a generalized Riemann problem between neighboring grid cells. A high-resolution wave-propagation algorithm is ...

Conservation laws with discontinuous flux

We consider an hyperbolic conservation law with discontinuous flux. Such partial differential equation arises in different applicative problems, in particular we are motivated by a model of traffic flow. We provide a new formulation in terms of Riemann Solvers. Moreover, we determine the class of Riemann Solvers which provide existence and uniqueness of the corresponding weak entropic solutions...

A numerical method for fractal conservation laws

We consider a fractal scalar conservation law, that is to say, a conservation law modified by a fractional power of the Laplace operator, and we propose a numerical method to approximate its solutions. We make a theoretical study of the method, proving in the case of an initial data belonging to L∞ ∩ BV that the approximate solutions converge in L∞ weak-∗ and in Lp strong for p < ∞, and we give...

A Numerical Method for Fractal Conservation Laws

We consider a fractal scalar conservation law, that is to say, a conservation law modified by a fractional power of the Laplace operator, and we propose a numerical method to approximate its solutions. We make a theoretical study of the method, proving in the case of an initial data belonging to L∞ ∩ BV that the approximate solutions converge in L∞ weak-∗ and in Lp strong for p < ∞, and we give...