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An artificial boundary condition for an advection–diffusion equation
Author(s) -
Lohéac JeanPierre
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140302
Subject(s) - mathematics , advection , viscosity , mathematical analysis , diffusion , boundary value problem , diffusion equation , space (punctuation) , mathematical physics , thermodynamics , physics , economy , economics , service (business) , linguistics , philosophy
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 − n (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 − n× 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 .