We introduce a scheme to compute the viscosity solution of the Riemannian Eikonal equation, on a regular grid or triangular mesh and which uses the order given by the Sweeping algorithm, to update the points. We also compute the bicharacteristic curves of the viscosity solution in a domain Omega in Eulerian way: instead of solving a system of...
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2003 (v1)PublicationUploaded on: March 31, 2023
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2018 (v1)Publication
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2016 (v1)Publication
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2003 (v1)Publication
We introduce a new homogenized hyperbolic (multiclass) traffic flow model, which allows us to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.) and drivers. We discretize the starting Lagrangian system introduced below with a Godunov scheme, and we let the mesh size h in (x, t) go to 0: the typical length...
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2014 (v1)Publication
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2003 (v1)Publication
We introduce a new homogenized hyperbolic (multiclass) traffic flow model which allows to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.). We discretize the system with a Godunov Lagrangian scheme with oscillating initial data which describe the non homogeneity of the traffic, and we study the...
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2006 (v1)Publication
In this Note we deal with the finite element approximation of a transmission problem across a prefractal curve approximating the von Koch fractal curve. We construct a mesh adapted to the geometric shape of the interface and we refine it consistently with some estimates in suitable weighted Sobolev spaces. In these spaces we also obtain an...
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2001 (v1)Publication
The aim of this work is the generation of anisotropic meshes which are automatically refined in some regions, typically where we want to solve numerically a PDE whose solution is singular. The basic idea is to consider an initial closed curve and to move this curve by the Hamilton-Jacobi equation on a manifold. Similar ideas could also be...
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2006 (v1)Publication
We introduce some models for vehicular traffic flow based on hyperbolic balance laws. We focus in particular on source terms for modeling highway entries and exits or local changes of the traffic flow due to inhomogeneities of the road. Rigorous well-posedness results and numerical investigations are presented. We show in particular how real...
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2014 (v1)Publication
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2013 (v1)Publication
In this paper we provide the piecewise linear Galerkin approximation of a second order transmission problem across a highly conductive prefractal layer of von Koch type. We firstly generate an appropriate mesh adapted to the geometric shape of the interface and then we construct a refinement algorithm consistent with a suitable estimate in...
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2016 (v1)Publication
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2017 (v1)Publication
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2005 (v1)Publication
We introduce a new framework for studying two-dimensional conservation laws by compensated compactness arguments. Our main result deals with 2D conservation laws which are nonlinear in the sense that their velocity fields are a.e. not co-linear. We prove that if $u^epsilon$ is a family of uniformly bounded approximate solutions of such...
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2007 (v1)Publication
We present a fast algorithm for path computation of multiple diffracted rays relevant to ray tracing techniques. The focus is on double diffracted rays, but generalizations are also mentioned. The novelty of our approach is in the use of an analytical geometry procedure which permits to re-write the problem as a simple nonlinear equation. This...
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2013 (v1)Publication
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2008 (v1)Publication
A numerical study on a non-linear hyperbolic diffusion equation is proposed. The Hartree hybrid method combining finite difference techniques with the method of characteristic is used in the presence of discontinuities between initial and boundary conditions. The technique proved to be an useful tool to overcome oscillation problems and...
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2016 (v1)Publication
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2005 (v1)Publication
This note discusses the role of source terms in the modeling of vehicular traffic through conservation laws. As is well known, a source term in the equation for the vehicular density may represent entries or exits. When a second conservation laws is present, suitable source terms may describe various inhomogeneities of the road, such as...
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2002 (v1)Publication
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Uploaded on: April 14, 2023