Related papers: Reconstruction of finite volume solution for param…
We study the convergence of a finite volume method based on the method of bicharacteristics for multidimensional hyperbolic conservation laws. In particular, we concentrate on the linear wave equation system and nonlinear Euler equations of…
We propose a model reduction procedure for rapid and reliable solution of parameterized hyperbolic partial differential equations. Due to the presence of parameter-dependent shock waves and contact discontinuities, these problems are…
We address the approximation of entropy solutions to initial-boundary value problems for nonlinear strictly hyperbolic conservation laws using neural networks. A general and systematic framework is introduced for the design of efficient and…
We proposed a piecewise quadratic reconstruction method in multiple dimensions, which is in an integrated style, for finite volume schemes to scalar conservation laws. This integrated quadratic reconstruction is parameter-free and…
We develop a high order reconstructed discontinuous approximation (RDA) method for solving a mixed formulation of the quad-curl problem in two and three dimensions. This mixed formulation is established by adding an auxiliary variable to…
In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…
We study solutions to nonlinear hyperbolic systems with fully nonlinear relaxation terms in the limit of, both, infinitely stiff relaxation and arbitrary late time. In this limit, the dynamics is governed by effective systems of parabolic…
This work aims to reconstruct image sequences with Total Variation regularity in super-resolution. We consider, in particular, images of scenes for which the point-to-point image transformation is a plane projective transformation. We first…
We derive conditional a priori error estimates of a wide class of finite volume and Runge-Kutta discontinuous Galerkin methods with abstract limiting for hyperbolic systems of conservation laws in 1D via the verification of weak consistency…
We propose an efficient residual minimization technique for the nonlinear model-order reduction of parameterized hyperbolic partial differential equations. Our nonlinear approximation space is a span of snapshots evaluated on a shifted…
The paper proposes a scheme by combining the Runge-Kutta discontinuous Galerkin method with a {\delta}-mapping algorithm for solving hyperbolic conservation laws with discontinuous fluxes. This hybrid scheme is particularly applied to…
We present a novel implementation of a genuinely $4^{\rm th}$-order accurate finite volume scheme for multidimensional classical and special relativistic magnetohydrodynamics (MHD) based on the constrained transport (CT) formalism. The…
We present a fourth-order accurate finite volume method for the solution of ideal magnetohydrodynamics (MHD). The numerical method combines high-order quadrature rules in the solution of semi-discrete formulations of hyperbolic conservation…
A theoretical framework and numerical techniques to solve optimal control problems with a spatial trace term in the terminal cost and governed by regularized nonlinear hyperbolic conservation laws are provided. Depending on the spatial…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
In this paper we construct high order finite volume schemes on networks of hyperbolic conservation laws with coupling conditions involving ODEs. We consider two generalized Riemann solvers at the junction, one of Toro-Castro type and a…
This paper investigates the problem of recovering source terms in abstract initial value problems (IVP) commonly used to model various scientific phenomena in physics, chemistry, economics, and other fields. We consider source terms of the…