Convergence and superconvergence analysis of finite element methods on graded meshes for singularly and semisingularly perturbed reaction-diffusion problems

Authors:
Guoqing Zhu;Shaochun Chen
Affiliations:
Department of Mathematics, Zhengzhou University, 450052 Zhengzhou, PR China;Department of Mathematics, Zhengzhou University, 450052 Zhengzhou, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Finite element approximation of convection diffusion problems using graded meshes

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Corrigendum: Corrigendum to "Uniformly convergent finite element methods for singularly perturbed elliptic boundary value problems I: Reaction-diffusion type" [Comput. Math. Appl. 35 (3) (1998) 57-70]

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Abstract

The bilinear finite element methods on appropriately graded meshes are considered both for solving singular and semisingular perturbation problems. In each case, the quasi-optimal order error estimates are proved in the @e-weighted H^1-norm uniformly in singular perturbation parameter @e, up to a logarithmic factor. By using the interpolation postprocessing technique, the global superconvergent error estimates in @e-weighted H^1-norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis.