Optimal rate of convergence of a stochastic particle method to solutions of 1D viscous scalar conservation laws

Rate of Convergence of a Particle Method for the Solution of a 1d Viscous Scalar Conservation Law in a Bounded Interval

The comparison of two high-order semi-discrete central schemes for solving hyperbolic conservation laws

This work presents two high-order, semi-discrete, central-upwind schemes for computing approximate solutions of 1D systems of conservation laws. We propose a central weighted essentially non-oscillatory (CWENO) reconstruction, also we apply a fourth-order reconstruction proposed by Peer et al., and afterwards, we combine these reconstructions with a semi-discrete central-upwind numerical flux ...

Long-time Behavior, Invariant Measures and Regularizing Effects for Stochastic Scalar Conservation Laws

We study the long-time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random in time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latter being new e...

Viscous Shock Wave Tracing, Local Conservation Laws, and Pointwise Estimates by Tai-ping Liu and Shih-hsien Yu

We introduce a new approach to decompose a system of viscous conservation laws with respect to each characteristic wave structures. Under this new decomposition, the global wave interactions of the system are reduced to coupling of nonlinear waves around constant states outside shock region and a scalar conservation law in the shock region to determine the behavior of local internal shock layer...

Fractional Rate of Convergence for Viscous Approximation to Nonconvex Conservation Laws

This paper considers the viscous approximations to conservation laws with nonconvex flux function. It is shown that if the entropy solutions are piecewise smooth, then the rate of L1convergence is a fractional number in (0.5, 1]. This is in contrast to the corresponding result for the convex conservation laws. Numerical experiments indicate that the theoretical prediction for the convergence ra...