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Pseudo‐transparent boundary conditions for the diffusion equation. Part I
Author(s) -
Joly P.,
Nedelec J. C.
Publication year - 1989
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.1670110602
Subject(s) - mathematics , convergence (economics) , diffusion equation , boundary (topology) , diffusion , mathematical analysis , space (punctuation) , boundary value problem , computer science , physics , economy , economic growth , economics , thermodynamics , service (business) , operating system
Abstract In this article, we introduce and study a family of artificial boundary conditions for the diffusion equation. These conditions are local in time and non‐local in space. We describe the principle of the approximation, show that the corresponding approximate problems are mathematically well‐posed and give convergence results, as well as error estimates, of the approximate solution to the exact one.