Analysis of the equilibrated residual method for a posteriori error estimation on meshes with hanging nodes

DOI10.1016/j.cma.2006.10.020zbMath1173.76424OpenAlexW2105402503MaRDI QIDQ1033363

Mark Ainsworth, Chang-Wan Kim, Leszek F. Demkowicz

Publication date: 6 November 2009

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

Full work available at URL: https://doi.org/10.1016/j.cma.2006.10.020

zbMATH Keywords

adaptive mesh refinementfinite element analysisa posteriori error estimatehanging nodesequilibrated fluxes

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10) Reaction effects in flows (76V05)

Related Items

Reliable and efficient equilibrated a posteriori finite element error control in elastoplasticity and elastoviscoplasticity with hardening, A smoothed finite element method for octree-based polyhedral meshes with large number of hanging nodes and irregular elements, Adaptive Computation with Splines on Triangulations with Hanging Vertices, Constraint-free adaptive FEMs on quadrilateral nonconforming meshes, Realistic computable error bounds for three-dimensional finite element analyses in linear elasticity, Adaptive \(hpq\) finite element methods for the analysis of 3D-based models of complex structures. Part II: A posteriori error estimation, Hanging nodes and XFEM, A posteriori error estimators for stabilized finite element approximations of an optimal control problem, Spline element methods allowing multiple level hanging nodes, Some a posteriori error bounds for numerical solutions of plate in bending problems, On the asymptotic exactness of error estimators based on the equilibrated residual method for quadrilateral finite elements, Hexahedral constraint-free finite element method on meshes with hanging nodes, Forward modelling of geophysical electromagnetic data on unstructured grids using an adaptive mimetic finite-difference method, An adjoint-based hp-adaptive stabilized finite-element method with shock capturing for turbulent flows, Novel quadtree algorithm for adaptive analysis based on cell-based smoothed finite element method

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A procedure for a posteriori error estimation for \(h\)-\(p\) finite element methods
• Toward a universal h-p adaptive finite element strategy. I: Constrained approximation and data structure
• A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
• Aspects of an adaptive \(hp\)-finite element method: Adaptive strategy, conforming approximation and efficient solvers
• A unified approach to a posteriori error estimation using element residual methods
• A general method for recovering equilibrating element tractions
• A Posteriori Error Estimators for the Stokes and Oseen Equations
• Some A Posteriori Error Estimators for Elliptic Partial Differential Equations
• The self-equilibration of residuals and complementarya posteriori error estimates in the finite element method
• Error Estimate Procedure in the Finite Element Method and Applications
• Reliable and Robust A Posteriori Error Estimation for Singularly Perturbed Reaction-Diffusion Problems
• A model study of element residual estimators for linear elliptic problems: The quality of the estimators in the interior of meshes of triangles and quadrilaterals
• Computation of Maxwell eigenvalues on curvilinear domains using hp-version Nédélec elements