Related papers: Solving One Dimensional Scalar Conservation Laws b…
A particle scheme for scalar conservation laws in one space dimension is presented. Particles representing the solution are moved according to their characteristic velocities. Particle interaction is resolved locally, satisfying exact…
An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is…
We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction…
We consider conservation laws on moving hypersurfaces. In this work the velocity of the surface is prescribed. But one may think of the velocity to be given by PDEs in the bulk phase. We prove existence and uniqueness for a scalar…
We present a fully discrete particle approximation for one-dimensional scalar conservation laws. Under suitable monotonicity assumptions on the macroscopic velocity, we construct a vacuum-compatible family of time-discrete particle…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
This paper presents applications of weighted meshless scheme for conservation laws to the Euler equations and the equations of ideal magnetohydrodynamics. The divergence constraint of the latter is maintained to the truncation error by a…
We prove the stability with respect to the flux of solutions to initial-boundary value problems for scalar non-autonomous conservation laws in one space dimension. Key estimates are obtained through a careful construction of the solutions.
We propose a new entropy-compatible neural network method for scalar hyperbolic conservation laws and establish, to our knowledge, the first explicit \(L^1\) convergence rates in this setting that apply to piecewise smooth entropy…
In this paper we study the finite time emergence of one shock for the solution of scalar conservation laws in one space dimension with general flux f . We give a necessary and sufficient condition to the initial data connecting to flux. The…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…
In this paper we present a novel framework for obtaining high-order numerical methods for scalar conservation laws in one-space dimension for both the homogeneous and non-homogeneous case. The numerical schemes for these two settings are…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along…
We develop deterministic particle schemes to solve non-local scalar conservation laws with congestion. We show that the discrete approximations converge to the unique entropy solution with an explicit rate of convergence under more general…
We introduce a robust first order accurate meshfree method to numerically solve time-dependent nonlinear conservation laws. The main contribution of this work is the meshfree construction of first order consistent summation by parts…
This paper discusses a connection between scalar convex conservation laws and Pontryagin's minimum principle. For flux functions for which an associated optimal control problem can be found, a minimum value solution of the conservation law…
We consider nondecreasing entropy solutions to 1-d scalar conservation laws and show that the spatial derivatives of such solutions satisfy a contraction property with respect to the Wasserstein distance of any order. This result extends…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
In this paper we present a novel framework for obtaining high order numerical methods for 1-D scalar conservation laws with non-convex flux functions. When solving Riemann problems, the Oleinik entropy condition, [16], is satisfied when the…