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

DOI10.1016/j.cam.2010.04.021zbMath1197.65172OpenAlexW2035809912MaRDI QIDQ984913

Guo-Qing Zhu, Shao-Chun Chen

Publication date: 20 July 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2010.04.021

zbMATH Keywords

singular perturbationerror estimatesnumerical experimentsfinite elementsuperconvergencegraded meshesself-adjoint elliptic boundary-value problems

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Singular perturbations in context of PDEs (35B25) Error bounds for boundary value problems involving PDEs (65N15) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

Related Items (6)

A posteriori error estimation based on conservative flux reconstruction for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem on anisotropic meshes ⋮ Energy-norm and balanced-norm supercloseness error analysis of a finite volume method on Shishkin meshes for singularly perturbed reaction-diffusion problems ⋮ Robust numerical methods for singularly perturbed differential equations: a survey covering 2008-2012 ⋮ High order multiplication perturbation method for singular perturbation problems ⋮ The finite volume element method on the Shishkin mesh for a singularly perturbed reaction-diffusion problem ⋮ Guaranteed a posteriori error estimates for nonconforming finite element approximations to a singularly perturbed reaction-diffusion problem

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