Finite volume approximation of elliptic problems and convergence of an approximate gradient

Authors
Eymard, R Gallouet, T Herbin, R
Citation
R. Eymard et al., Finite volume approximation of elliptic problems and convergence of an approximate gradient, APPL NUM M, 37(1-2), 2001, pp. 31-53
Citations number
41
Categorie Soggetti
Mathematics
Journal title
APPLIED NUMERICAL MATHEMATICS
ISSN journal
01689274 → ACNP
Volume
37
Issue
1-2
Year of publication
2001
Pages
31 - 53
Database
ISI
SICI code
0168-9274(200104)37:1-2<31:FVAOEP>2.0.ZU;2-3
Abstract
Using a classical finite volume piecewise constant approximation of the sol ution of an elliptic problem in a domain Omega, we build here an approximat e gradient of the solution. It is then shown that this approximate gradient converges in H-div(Omega). An error estimate is given when the solution be longs to H-2(Omega). (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.