Superconvergence and recovery type a posteriori error estimation for hybrid stress finite element method

DOI10.1007/s11425-016-5144-3zbMath1388.74091arXiv1502.01099OpenAlexW2329901198MaRDI QIDQ341362

YongKe Wu, Xiaoping Xie, Yan-hong Bai

Publication date: 16 November 2016

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1502.01099

zbMATH Keywords

linear elasticitysuperconvergencea posteriori error estimatorrecoveryhybrid stress finite element

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Finite element methods applied to problems in solid mechanics (74S05) 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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• Uniform convergence and a posteriori error estimation for assumed stress hybrid finite element methods
• State-of-the-art development of hybrid/mixed finite element method
• New mixed finite elements for plane elasticity and Stokes equations
• The patch recovery for finite element approximation of elasticity problems under quadrilateral meshes
• A convergence condition for the quadrilateral Wilson element
• A new superconvergence property of Wilson nonconforming finite element
• Superconvergence results on mildly structured triangulations
• An alternative version of the Pian-Sumihara element with a simple extension to nonlinear problems
• A unified analysis for stress/strain hybrid methods of high performance.
• Quadrilateral mesh revisited.
• Superconvergence in Galerkin finite element methods
• A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids
• The polynomial-preserving recovery for higher order finite element methods in 2D and 3D
• Combined hybrid approach to finite element schemes of high performance
• Rational approach for assumed stress finite elements
• Superconvergence of quadratic finite elements on mildly structured grids
• Superconvergence and Reduced Integration in the Finite Element Method
• The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique
• Estimation of the Interpolation Error for Quadrilateral Finite Elements Which Can Degenerate into Triangles
• Superconvergence of Mixed Finite Element Approximations over Quadrilaterals
• Analysis of Some Quadrilateral Nonconforming Elements for Incompressible Elasticity
• Asymptotically Exact A Posteriori Error Estimators, Part I: Grids with Superconvergence
• Asymptotically Exact A Posteriori Error Estimators, Part II: General Unstructured Grids
• Optimization of stress modes by energy compatibility for 4-node hybrid quadrilaterals
• Approximation by quadrilateral finite elements
• Hybrid and Incompatible Finite Element Methods
• Ultraconvergence of the patch recovery technique II
• Superconvergence for the Gradient of Finite Element Approximations byL²Projections
• Superconvergence in Finite Element Methods and Meshes That are Locally Symmetric with Respect to a Point
• A New Finite Element Gradient Recovery Method: Superconvergence Property

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