Advances in Differential Equations

Singular perturbation of semi-linear reaction-convection equations in a channel and numerical applications

Chang-Yeol Jung and Du Pham

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

In this article, we investigate a way to analyze and approximate singularly perturbed convection-diffusion equations in a channel domain when a nonlinear reaction term with polynomial growth is present. We verify that the boundary layer structures are governed by certain simple recursive linear equations and this simplicity implies explicit pointwise and norm estimates. Furthermore, we can utilize the boundary layer structures (elements) in the finite elements discretizations which lead to the stability in the approximating systems and accurate approximation solutions with an economical mesh design, i.e., uniform mesh.

Article information

Source
Adv. Differential Equations Volume 12, Number 3 (2007), 265-300.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355867465

Mathematical Reviews number (MathSciNet)
MR2296568

Zentralblatt MATH identifier
1163.65053

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35B25: Singular perturbations 65N30: Finite elements, Rayleigh-Ritz and Galerkin methods, finite methods

Citation

Jung, Chang-Yeol; Pham, Du. Singular perturbation of semi-linear reaction-convection equations in a channel and numerical applications. Adv. Differential Equations 12 (2007), no. 3, 265--300. https://projecteuclid.org/euclid.ade/1355867465.


Export citation