Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method. II

DOI10.1016/S0045-7825(98)00010-3zbMath0941.65116OpenAlexW2150140956MaRDI QIDQ1971441

Zhimin Zhang, Jianzhong Zhu

Publication date: 10 August 2000

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(98)00010-3

zbMATH Keywords

finite element methodsuperconvergencea posteriori error estimatorleast-squares fittingtensor product elementspatch recovery techniques

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

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Cites Work

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• On superconvergence techniques
• The superconvergent patch recovery (SPR) and adaptive finite element refinement
• Analysis of the superconvergent patch recovery technique and a posteriori error estimator in the finite element method. I.
• Superconvergence for Galerkin methods for the two point boundary problem via local projections
• Superconvergence of the Velocity Along the Gauss Lines in Mixed Finite Element Methods
• Superconvergent Recovery of the Gradient from Piecewise Linear Finite-element Approximations
• Superconvergence of the gradient for quadratic triangular finite elements
• Superconvergence and Reduced Integration in the Finite Element Method
• 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
• Higher Order Local Accuracy by Averaging in the Finite Element Method
• Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration
• Local and global smoothing of discontinuous finite element functions using a least squares method
• On the calculation of consistent stress distributions in finite element approximations
• An Optimal $L_\infty $ Error Estimate for Galerkin Approximations to Solutions of Two-Point Boundary Value Problems
• Superconvergent recovery of gradients on subdomains from piecewise linear finite‐element approximations
• Superconvergence of the gradient of Galerkin approximations for elliptic problems

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