An artificial boundary condition for an advection–diffusion equation

✍ Scribed by Jean-Pierre Lohéac

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 731 KB
• Volume: 14
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670140302

✦ Synopsis

Abstract

Consider the advection–diffusion equation: u~1~ + au~x1~ − vδu = 0 in ℝ^n^ × ℝ^+^ with initial data u^0^; the Support of u^0^ is contained in ℝ(x~1~ < 0) and a: ℝ^n^ → ℝ is positive. In order to approximate the full space solution by the solution of a problem in ℝ × ℝ^+^, we propose the artificial boundary condition: u~1~ + au~x1~ = 0 on ∑. We study this by means of a transmission problem: the error is an O(v^2^) for small values of the viscosity v.