Related papers: Solving Random Hyperbolic Conservation Laws Using …
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…
We revisit the method of characteristics for shock wave solutions to nonlinear hyperbolic problems and we describe a novel numerical algorithm - the convex hull algorithm (CHA) - in order to compute, both, entropy dissipative solutions…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
In many applications, for instance when describing dynamics of fluids or gases, hyperbolic conservation laws arise naturally in the modeling of conserved quantities of a system, like mass or energy. These types of equations exhibit highly…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
We propose a general strategy for enforcing multiple conservation laws and dissipation inequalities in the numerical solution of initial value problems. The key idea is to represent each conservation law or dissipation inequality by means…
Godunov type numerical schemes for the class of hyperbolic systems, admitting non-classical $\delta-$ shocks are proposed. It is shown that the numerical approximations converge to the solution and preserve the physical properties of the…
Numerical schemes for the general relativistic hydrodynamic equations are discussed. The use of conservative algorithms based upon the characteristic structure of those equations, developed during the last decade building on ideas first…
We introduce stabilized spline collocation schemes for the numerical solution of nonlinear, hyperbolic conservation laws. A nonlinear, residual-based viscosity stabilization is combined with a projection stabilization-inspired linear…
Energy methods for constructing time-stepping algorithms are of increased interest in application to nonlinear problems, since numerical stability can be inferred from the conservation of the system energy. Alternatively, symplectic…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
We derive entropy conserving and entropy dissipative overlapping domain formulations for systems of nonlinear hyperbolic equations in conservation form, such as would be approximated by overset mesh methods. The entropy conserving…
We propose a numerical method to solve parameter-dependent hyperbolic partial differential equations (PDEs) with a moment approach, based on a previous work from Marx et al. (2020). This approach relies on a very weak notion of solution of…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
We revisit a well-established model for highly re-entrant semi-conductor manufacturing systems, and analyze it in the setting of states, in- and outfluxes being Borel measures. This is motivated by the lack of optimal solutions in the…
It is well known that for solutions of semi-linear parabolic PDEs, there are equivalent probabilistic interpretations, which yields the so called nonlinear Feymman-Kac formula. By adopting such formula, we consider in this work a novel…
We present a novel positive kinetic scheme built on the efficient collide-and-stream algorithm of the lattice Boltzmann method (LBM) to address hyperbolic conservation laws. We focus on the compressible Euler equations with strong…
Conservation laws are key theoretical and practical tools for understanding, characterizing, and modeling nonlinear dynamical systems. However, for many complex systems, the corresponding conserved quantities are difficult to identify,…
In this work, we introduce a novel approach to formulating an artificial viscosity for shock capturing in nonlinear hyperbolic systems by utilizing the property that the solutions of hyperbolic conservation laws are not reversible in time…
We show a novel systematic way to construct conservative finite difference schemes for quasilinear first-order system of ordinary differential equations with conserved quantities. In particular, this includes both autonomous and…