Related papers: Asymptotic-preserving schemes for the initial-boun…
This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…
The behavior of solutions to an initial boundary value problem for a hyperbolic system with relaxation is studied when the relaxation parameter is small, by using the method of Fourier Series and the energy method.
An initial boundary value problem for one-dimensional hyperbolic compressible Navier-Stokes equations is investigated. After transforming the system into Lagrangian coordinate, the resulting system possesses a structure with uniform…
In this article, we consider linear hyperbolic Initial and Boundary Value Problems (IBVP) in a rectangle (or possibly curvilinear polygonal domains) in both the constant and variable coefficients cases. We use semigroup method instead of…
In this paper well-posedness is proved for an initial and boundary value problem (IBVP) relative to a large class of quasilinear hyperbolic systems, in $p+q$ equations, on a strip, arising from a model of $H_2O$-phase transitions in the…
In this paper, we introduce a hyperbolic model for entropy dissipative system of viscous conservation laws via a flux relaxation approach. We develop numerical schemes for the resulting hyperbolic relaxation system by employing the…
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…
The initial-boundary value problem (IBVP) for the Maxwell-Bloch equations with an arbitrary inhomogeneous broadening and periodic boundary condition is studied. This IBVP describes the propagation of an electromagnetic wave generated by…
This work is devoted to the numerical simulation of a Vlasov-Poisson model describing a charged particle beam under the action of a rapidly oscillating external electric field. We construct an Asymptotic Preserving numerical scheme for this…
In this contribution we present recent developments in the formulation and solution of Initial Boundary Value Problems (IBVPs). Building upon a modern variational action formulation of classical dynamics, we treat Initial Boundary Value…
This paper is a continuation of our preceding work on hyperbolic relaxation systems with characteristic boundaries of type I. Here we focus on the characteristic boundaries of type II, where the boundary is characteristic for the…
The main purpose of the present paper is to study from a numerical analysis point of view some robust methods designed to cope with stiff (highly anisotropic) elliptic problems. The so-called asymptotic-preserving schemes studied in this…
We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently…
We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In…
We study the convergence of a class of asymptotic preserving numerical schemes initially proposed by F. Filbet & S. Jin \cite{filb1} and G. Dimarco & L. Pareschi \cite{DimarcoP} in the context of nonlinear and stiff kinetic equations. Here,…
The concern of the present work is the introduction of a very efficient Asymptotic Preserving scheme for the resolution of highly anisotropic diffusion equations. The characteristic features of this scheme are the uniform convergence with…
We develop an asymptotic-preserving scheme to solve evolution problems containing stiff transport terms. This scheme is based to a micro-macro decomposition of the unknown, coupled with a stabilization procedure. The numerical method is…
The present paper introduces an efficient and accurate numerical scheme for the solution of a highly anisotropic elliptic equation, the anisotropy direction being given by a variable vector field. This scheme is based on an asymptotic…
We consider the rigorous derivation of asymptotic formulas for initial-boundary value problems using the nonlinear steepest descent method. We give detailed derivations of the asymptotics in the similarity and self-similar sectors for the…
We consider hyperbolic systems of conservation laws with relaxation source terms leading to a diffusive asymptotic limit under a parabolic scaling. We introduce a new class of secondorder in time and space numerical schemes, which are…