Displaying similar documents to “Analyzing the dynamics of the forced Burgers equation.”

Convergence to the travelling wave solution for a nonlinear reaction-diffusion equation

Shoshana Kamin, Philip Rosenau (2004)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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We study the behaviour of the solutions of the Cauchy problem u t = u m x ⁢ x + u ⁢ 1 - u m - 1 , x ∈ R , t > 0 ⁢ u ⁢ 0 , x = u 0 ⁢ x , u 0 ⁢ x ≥ 0 , and prove that if initial data u 0 ⁢ x decay fast enough at infinity then the solution of the Cauchy problem approaches the travelling wave solution spreading either to the right or to the left, or two travelling waves moving in opposite directions. Certain generalizations are also mentioned.

Error estimates for barycentric finite volumes combined with nonconforming finite elements applied to nonlinear convection-diffusion problems

Vít Dolejší, Miloslav Feistauer, Jiří Felcman, Alice Kliková (2002)

Applications of Mathematics

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The subject of the paper is the derivation of error estimates for the combined finite volume-finite element method used for the numerical solution of nonstationary nonlinear convection-diffusion problems. Here we analyze the combination of barycentric finite volumes associated with sides of triangulation with the piecewise linear nonconforming Crouzeix-Raviart finite elements. Under some assumptions on the regularity of the exact solution, the L 2 ( L 2 ) and L 2 ( H 1 ) error estimates are established....

Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model

Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

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Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous...