Related papers: Finite volume schemes on Lorentzian manifolds
Following Ben-Artzi and LeFloch, we consider nonlinear hyperbolic conservation laws posed on a Riemannian manifold, and we establish an L1-error estimate for a class of finite volume schemes allowing for the approximation of entropy…
We consider nonlinear hyperbolic conservation laws, posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and in which the "flux" is defined as a flux field of n-forms depending on a parameter (the unknown…
We study nonlinear hyperbolic conservation laws posed on a differential (n+1)-manifold with boundary referred to as a spacetime, and defined from a prescribed flux field of n-forms depending on a parameter (the unknown variable), a class of…
We consider entropy solutions to the initial value problem associated with scalar nonlinear hyperbolic conservation laws posed on the two-dimensional sphere. We propose a finite volume scheme which relies on a web-like mesh made of segments…
This paper addresses the three concepts of \textit{ consistency, stability and convergence } in the context of compact finite volume schemes for systems of nonlinear hyperbolic conservation laws. The treatment utilizes the framework of…
We introduce a formulation of the initial and boundary value problem for nonlinear hyperbolic conservation laws posed on a differential manifold endowed with a volume form, possibly with a boundary; in particular, this includes the…
This paper studies finite volume schemes for scalar hyperbolic conservation laws on evolving hypersurfaces of $\mathbb{R}^3$. We compare theoretical schemes assuming knowledge of all geometric quantities to (practical) schemes defined on…
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws posed on a (Riemannian or Lorentzian) manifold. The flux of…
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) property to manifolds, by deriving conditions on the flux of…
We build a finite volume scheme for the scalar conservation law $\partial_t u + \partial_x (H(x, u)) = 0$ with bounded initial condition for a wide class of flux function $H$, convex with respect to the second variable. The main idea for…
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…
We prove that a class of monotone finite volume schemes for scalar conservation laws with discontinuous flux converge at a rate of $\sqrt{\Delta x}$ in $\mathrm{L}^1$, whenever the flux is strictly monotone in $u$ and the spatial dependency…
We consider a hyperbolic conservation law posed on an (N+1)-dimensional spacetime, whose flux is a field of differential forms of degree N. Generalizing the classical Kuznetsov's method, we derive an L1 error estimate which applies to a…
We consider a class of doubly nonlinear degenerate hyperbolic-parabolic equations with homogeneous Dirichlet boundary conditions, for which we first establish the existence and uniqueness of entropy solutions. We then turn to the…
In this article, we discuss the error analysis for a certain class of monotone finite volume schemes approximating nonlocal scalar conservation laws, modeling traffic flow and crowd dynamics, without any additional assumptions on…
We illustrate that numerical solutions of high order finite volume Hermite weighted essentially non-oscillatory (HWENO) scheme for some nonconvex conservation laws perform poorly or converge to the entropy solution in a slow speed. The…
We prove the convergence of the explicit-in-time Finite Volume method with monotone fluxes for the approximation of scalar first-order conservation laws with multiplicative, compactly supported noise.
We study the finite volume approximation of strong solutions to nonlinear systems of conservation laws. We focus on time-explicit schemes on unstructured meshes, with entropy satisfying numerical fluxes. The numerical entropy dissipation is…
We present a class of numerical schemes for two-dimensional systems of nonlocal conservation laws, which are based on utilizing well-known monotone numerical flux functions after suitably approximating the nonlocal terms. The considered…