Related papers: Solving Random Hyperbolic Conservation Laws Using …
This paper presents a structure-preserving spatial discretization method for distributed parameter port-Hamiltonian systems. The class of considered systems are hyperbolic systems of two conservation laws in arbitrary spatial dimension and…
An effective algorithmic method is presented for finding the local conservation laws for partial differential equations with any number of independent and dependent variables. The method does not require the use or existence of a…
The trapezoidal rule, which is a special case of the Newmark family of algorithms, is one of the most widely used methods for transient hyperbolic problems. In this work, we show that this rule conserves linear and angular momenta and…
We consider conservation laws with nonlocal velocity and show for nonlocal weights of exponential type that the unique solutions converge in a weak or strong sense (dependent on the regularity of the velocity) to the entropy solution of the…
We propose a nonlinear registration-based model reduction procedure for rapid and reliable solution of parameterized two-dimensional steady conservation laws. This class of problems is challenging for model reduction techniques due to the…
In this work we present a rather general approach to approximate the solutions of nonlocal conservation laws. In a first step, we approximate the nonlocal term with an appropriate quadrature rule applied to the spatial discretization. Then,…
We consider hyperbolic systems of conservation laws in one spatial dimension. For any limit of front tracking solutions $v$, and for a general weak solution $u\in L^\infty$ with no BV assumption, we prove the following H\"older-type…
In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. Standard intrusive methods lead to oscillatory solutions which sometimes even cause the loss of hyperbolicity. We…
We develop a new numerical method for approximating the infinite time reachable set of strictly stable linear control systems. By solving a linear program with a constraint that incorporates the system dynamics, we compute a polytope with…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
The method of distributions is developed for systems that are governed by hyperbolic conservation laws with stochastic forcing. The method yields a deterministic equation for the cumulative density distribution (CDF) of a system state,…
Fast sweeping methods have become a useful tool for computing the solutions of static Hamilton-Jacobi equations. By adapting the main idea behind these methods, we describe a new approach for computing steady state solutions to systems of…
This paper introduces a novel wave front tracking framework for reconstructing unknown flux functions in $2\times 2$ hyperbolic conservation laws, extending beyond the well-studied scalar case. By analyzing Riemann solutions at fixed…
We have developed a new embedding method for solving scalar hyperbolic conservation laws on surfaces. The approach represents the interface implicitly by a signed distance function following the typical level set method and some embedding…
This work examines the development of an entropy conservative (for smooth solutions) or entropy stable (for discontinuous solutions) space-time discontinuous Galerkin (DG) method for systems of non-linear hyperbolic conservation laws. The…
This paper deals with a splitting method applied to a conservation law model of manufacturing system incorporating yield loss. A splitting scheme has been proposed. The yield loss term is treated by solving implicitly an ordinary…
In this work we introduce the obstacle-mass constraint problem for a multidimensional scalar hyperbolic conservation law. We prove existence of an entropy solution to this problem by a penalization/viscosity method. The mass constraint…
We construct entropy conservative and entropy stable high order accurate discontinuous Galerkin (DG) discretizations for time-dependent nonlinear hyperbolic conservation laws on curvilinear meshes. The resulting schemes preserve a…
In this paper, we consider $2 \times 2$ hyperbolic systems of conservation laws in one space dimension with characteristic fields satisfying a condition that encompasses genuine nonlinearity and linear degeneracy as well as intermediate…
A hyperbolic system must have a set of linearly independent eigenvectors and corresponding real eigenvalues. In numerical simulations, however, the eigenvalues can be complex because truncation errors pollute a characteristic polynomial of…