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Stability and convergence of a Galerkin‐characteristics finite element scheme of lumped mass type
Author(s) -
Pironneau O.,
Tabata M.
Publication year - 2010
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.2459
Subject(s) - finite element method , mathematics , galerkin method , discontinuous galerkin method , convergence (economics) , robustness (evolution) , scheme (mathematics) , triangulation , norm (philosophy) , mathematical analysis , convection , geometry , mechanics , physics , engineering , structural engineering , biochemistry , chemistry , political science , law , economics , gene , economic growth
A Galerkin‐characteristics finite element scheme of lumped mass type is presented for the convection–diffusion problems. Under the weakly acute triangulation hypothesis the scheme is proved to be stable and convergent in the L ∞ ‐norm. Using the Freefem, we show 2D and 3D numerical examples, which reflect the robustness of the scheme and the theoretical convergence result. Copyright © 2010 John Wiley & Sons, Ltd.