Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM

DOI10.1090/S0025-5718-02-01412-6zbMath0997.65127MaRDI QIDQ4529704

Sören Bartels, Carsten Carstensen

Publication date: 6 May 2002

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

zbMATH Keywords

finite element methodreliabilityadaptive algorithmunstructured gridsaveraging techniquea posteriori error estimateshigher-order finite element methodnumerial examplesresidual based error estimate

Mathematics Subject Classification ID

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

Related Items (22)

Reliable averaging for the primal variable in the Courant FEM and hierarchical error estimators on red-refined meshes ⋮ Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM ⋮ Flexible patch post-processing recovery strategies for solution enhancement and adaptive mesh refinement ⋮ Reliability and efficiency of an anisotropic Zienkiewicz-Zhu error estimator ⋮ Axioms of adaptivity ⋮ All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable ⋮ Adaptive boundary element methods. A posteriori error estimators, adaptivity, convergence, and implementation ⋮ The superconvergent cluster recovery method ⋮ Hierarchical a posteriori error estimation of Bank-Weiser type in the FEniCS project ⋮ Recovery strategies, a posteriori error estimation, and local error indication for second‐order G/XFEM and FEM ⋮ A posteriori error estimates for nonconforming finite element methods for fourth-order problems on rectangles ⋮ ZZ-type a posteriori error estimators for adaptive boundary element methods on a curve ⋮ Adaptive Finite Element Solution of Variational Inequalities with Application in Contact Problems ⋮ Convergence and optimal complexity of adaptive finite element eigenvalue computations ⋮ Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis ⋮ Averaging techniques yield reliable a posteriori finite element error control for obstacle problems ⋮ A unifying theory of a posteriori finite element error control ⋮ On computational methods for variational inequalities. Consistent error estimation of FE-approximation ⋮ Zienkiewicz–Zhu error estimators on anisotropic tetrahedral and triangular finite element meshes ⋮ An hp‐adaptive finite element model for heat transfer within partitioned enclosures ⋮ On adaptive computational methods: global norms controlling local errors ⋮ An inexact ℓ₁penalty SQP algorithm for PDE-constrained optimization with an application to shape optimization in linear elasticity

Uses Software

• na14

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The partition of unity finite element method: basic theory and applications
• Remarks around 50 lines of Matlab: short finite element implementation
• The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines
• Finite Element Methods for Navier-Stokes Equations
• A simple error estimator and adaptive procedure for practical engineerng analysis
• Validation of a posteriori error estimators by numerical approach
• Some remarks on Zienkiewicz‐Zhu estimator
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
• A Posteriori Error Estimators for the Raviart–Thomas Element
• Finite elements. Theory, fast solvers and applications in elasticity theory
• A posteriori error estimate and h-adaptive algorithm on surfaces from Symm's integral equation

This page was built for publication: Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM