Superconvergence analysis of the linear finite element method and a gradient recovery postprocessing on anisotropic meshes

DOI10.1090/S0025-5718-2014-02846-9zbMath1305.65226OpenAlexW2066488364MaRDI QIDQ5497017

Weiming Cao

Publication date: 30 January 2015

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-2014-02846-9

zbMATH Keywords

superconvergenceelliptic problemsanisotropic meshlinear finite elementpost processingrecovery type error estimates

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) 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)

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Polynomial preserving recovery on boundary ⋮ Anisotropic adaptive finite elements for an elliptic problem with strongly varying diffusion coefficient ⋮ Hessian recovery for finite element methods ⋮ Superconvergent gradient recovery for nonlinear Poisson-Nernst-Planck equations with applications to the ion channel problem

Cites Work

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• An anisotropic unstructured triangular adaptive mesh algorithm based on error and error gradient information
• Anisotropic error estimates for elliptic problems
• Superconvergence results on mildly structured triangulations
• Superconvergence in Galerkin finite element methods
• Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator
• Optimal anisotropic meshes for minimizing interpolation errors in $L^p$-norm
• Polynomial preserving recovery for meshes from Delaunay triangulation or with high aspect ratio
• Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?
• Simple nonconforming quadrilateral Stokes element
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity
• An Anisotropic Error Indicator Based on Zienkiewicz--Zhu Error Estimator: Application to Elliptic and Parabolic Problems
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• Anisotropic mesh adaptation: towards user-independent, mesh-independent and solver-independent CFD. Part I: general principles
• Uniform Convergence and Superconvergence of Mixed Finite Element Methods on Anisotropically Refined Grids
• A Posteriori Error Estimates Based on the Polynomial Preserving Recovery
• Numerical study of the effectivity index for an anisotropic error indicator based on Zienkiewicz-Zhu error estimator
• Analysis of recovery type a posteriori error estimators for mildly structured grids
• An Interpolation Error Estimate on Anisotropic Meshes in ${\mathcalR}^{n}$ and Optimal Metrics for Mesh Refinement
• A New Finite Element Gradient Recovery Method: Superconvergence Property
• An interpolation error estimate in $\mathcal{R}^2$ based on the anisotropic measures of higher order derivatives
• Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes
• On the Error of Linear Interpolation and the Orientation, Aspect Ratio, and Internal Angles of a Triangle
• Gradient recovery type a posteriori error estimates for finite element approximations on irregular meshes
• New anisotropic a priori estimates
• Optimal meshes for finite elements of arbitrary order

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