Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems

Authors:
Guoqing Zhu;Shaochun Chen
Affiliations:
School of Science, Beijing Institute of Technology, Beijing 100081, PR China;Department of Mathematics, Zhengzhou University, Zhengzhou 450052, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2010

Citing 8
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Anisotropic mesh refinement for a singularly perturbed reaction diffusion model problem

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Convergence and superconvergence analysis of finite element methods on highly nonuniform anisotropic meshes for singularly perturbed reaction—diffusion problems

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Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids

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Anisotropic interpolations with application to nonconforming elements

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Finite element approximation of convection diffusion problems using graded meshes

Applied Numerical Mathematics - Selected papers from the first Chilean workshop on numerical analysis of partial differential equations (WONAPDE 2004)
Convergence and superconvergence analysis of finite element methods on graded meshes for singularly and semisingularly perturbed reaction-diffusion problems

Journal of Computational and Applied Mathematics
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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Supercloseness on graded meshes for Q1 finite element approximation of a reaction-diffusion equation

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Abstract

The numerical approximation by a lower order anisotropic nonconforming finite element on appropriately graded meshes are considered for solving singular perturbation problems. The quasi-optimal order error estimates are proved in the @e-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 @e-weighted H^1-norm are obtained. Numerical experiments are given to demonstrate validity of our theoretical analysis.