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Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for semisingularly perturbed reaction–diffusion problems
Author(s) -
Zhu Guoqing,
Chen Shaochun
Publication year - 2008
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.978
Subject(s) - superconvergence , mathematics , finite element method , norm (philosophy) , perturbation (astronomy) , logarithm , singular perturbation , mathematical analysis , uniform convergence , polygon mesh , rate of convergence , numerical analysis , interpolation (computer graphics) , reaction–diffusion system , error analysis , convergence (economics) , geometry , channel (broadcasting) , computer graphics (images) , law , economic growth , computer network , bandwidth (computing) , computer science , engineering , quantum mechanics , political science , thermodynamics , animation , physics , electrical engineering , economics
The numerical approximation by a lower‐order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving semisingular perturbation problems. The quasi‐optimal‐order error estimates are proved in the ε‐weighted H 1 ‐norm valid uniformly, up to a logarithmic factor, in the singular perturbation parameter. By using the interpolation postprocessing technique, the global superconvergent error estimates in ε‐weighted H 1 ‐norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis. Copyright © 2007 John Wiley & Sons, Ltd.