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High accuracy analysis of the characteristic‐nonconforming FEM for a convection‐dominated transport problem
Author(s) -
Shi Dongyang,
Guan Hongbo,
Gong Wei
Publication year - 2013
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.2873
Subject(s) - superconvergence , mathematics , finite element method , convection–diffusion equation , interpolation (computer graphics) , norm (philosophy) , convection , consistency (knowledge bases) , projection (relational algebra) , operator (biology) , mathematical analysis , algorithm , geometry , computer science , mechanics , animation , physics , computer graphics (images) , political science , law , biochemistry , chemistry , repressor , transcription factor , gene , thermodynamics
A low order characteristic‐nonconforming E Q 1 rotfinite element method is proposed for solving a two‐dimensional convection‐dominated transport problem. On the basis of the distinguish property of E Q 1 rotelement, that is, the consistency error can be estimated as order O ( h 2 ), one order higher than that of its interpolation error, the superclose result in broken energy norm is derived for the fully discrete scheme. In the process, we use the interpolation operator instead of the so‐called elliptic projection, which is an indispensable tool in the traditional finite element analysis. Furthermore, the global superconvergence is obtained by using the interpolated postprocessing technique. Lastly, some numerical experiments are provided to verify our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.