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The waiting time property for parabolic problems trough the nondiffusion of support for the stationary problems.

Luis Alvarez, Jesús Ildefonso Díaz (2003)

RACSAM

In this note we study the waiting time phenomenon for local solutions of the nonlinear diffusion equation through its connection with the nondiffusion of the support property for local solutions of the family of discretized elliptic problems. We show that, under a suitable growth condition on the initial datum near the boundary of its support, a finite part of the family of solutions of the discretized problem maintain unchanged its support.

Theoretical analysis of the upwind finite volume scheme on the counter-example of Peterson

Daniel Bouche, Jean-Michel Ghidaglia, Frédéric P. Pascal (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

When applied to the linear advection problem in dimension two, the upwind finite volume method is a non consistent scheme in the finite differences sense but a convergent scheme. According to our previous paper [Bouche et al., SIAM J. Numer. Anal.43 (2005) 578–603], a sufficient condition in order to complete the mathematical analysis of the finite volume scheme consists in obtaining an estimation of order p, less or equal to one, of a quantity that depends only on the mesh and on the advection ...

Theoretical and numerical comparison of some sampling methods for molecular dynamics

Eric Cancès, Frédéric Legoll, Gabriel Stoltz (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

The purpose of the present article is to compare different phase-space sampling methods, such as purely stochastic methods (Rejection method, Metropolized independence sampler, Importance Sampling), stochastically perturbed Molecular Dynamics methods (Hybrid Monte Carlo, Langevin Dynamics, Biased Random Walk), and purely deterministic methods (Nosé-Hoover chains, Nosé-Poincaré and Recursive Multiple Thermostats (RMT) methods). After recalling some theoretical convergence properties for the...

Theoretical and numerical studies of the P N P M DG schemes in one space dimension

Abdulatif Badenjki, Gerald G. Warnecke (2019)

Applications of Mathematics

We give a proof of the existence of a solution of reconstruction operators used in the P N P M DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the P N P M DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several P N P M DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect the efficiency...

Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix, Philippe Féat, Francisco-Javier Sayas (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Theoretical and numerical study of a free boundary problem by boundary integral methods

Michel Crouzeix, Philippe Féat, Francisco-Javier Sayas (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper we study a free boundary problem appearing in electromagnetism and its numerical approximation by means of boundary integral methods. Once the problem is written in a equivalent integro-differential form, with the arc parametrization of the boundary as unknown, we analyse it in this new setting. Then we consider Galerkin and collocation methods with trigonometric polynomial and spline curves as approximate solutions.

Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping

R. Belaouar, T. Colin, G. Gallice, C. Galusinski (2006)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the...

Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping

R. Belaouar, T. Colin, G. Gallice, C. Galusinski (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for...

Theoretical aspects and numerical computation of the time-harmonic Green's function for an isotropic elastic half-plane with an impedance boundary condition

Mario Durán, Eduardo Godoy, Jean-Claude Nédélec (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

This work presents an effective and accurate method for determining, from a theoretical and computational point of view, the time-harmonic Green's function of an isotropic elastic half-plane where an impedance boundary condition is considered. This method, based on the previous work done by Durán et al. (cf. [Numer. Math.107 (2007) 295–314; IMA J. Appl. Math.71 (2006) 853–876]) for the Helmholtz equation in a half-plane, combines appropriately analytical and numerical techniques, which has an important...

Theory and numerical approximations for a nonlinear 1 + 1 Dirac system

Nikolaos Bournaveas, Georgios E. Zouraris (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.

Theory and numerical approximations for a nonlinear 1 + 1 Dirac system

Nikolaos Bournaveas, Georgios E. Zouraris (2012)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a nonlinear Dirac system in one space dimension with periodic boundary conditions. First, we discuss questions on the existence and uniqueness of the solution. Then, we propose an implicit-explicit finite difference method for its approximation, proving optimal order a priori error estimates in various discrete norms and showing results from numerical experiments.

Thermal ablation modeling via the bioheat equation and its numerical treatment

Agnieszka Bartłomiejczyk, Henryk Leszczyński, Artur Poliński (2015)

Applicationes Mathematicae

The phenomenon of thermal ablation is described by Pennes' bioheat equation. This model is based on Newton's law of cooling. Many approximate methods have been considered because of the importance of this issue. We propose an implicit numerical scheme which has better stability properties than other approaches.

Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion

Sören Bartels, Tomáš Roubíček (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting also plasticity with hardening and coupled with heat-transfer through dissipative heat production by viscoplastic effects and through thermal expansion and corresponding adiabatic effects. Numerical discretization of the thermodynamically consistent model is proposed by implicit time discretization, suitable regularization, and finite elements in space. Fine a-priori estimates are derived, and convergence is proved by careful successive...

Currently displaying 401 – 420 of 543