Averaging techniques yield reliable a posteriori finite element error control for obstacle problems

DOI10.1007/s00211-004-0553-6zbMath1063.65050OpenAlexW1995315828MaRDI QIDQ706593

Sören Bartels, Carsten Carstensen

Publication date: 8 February 2005

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00211-004-0553-6

zbMATH Keywords

variational inequalitiesnumerical examplesfinite elementerror estimatesecond order elliptic obstacle boundary value problems

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Newton-type methods (49M15)

Related Items

Space adaptive finite element methods for dynamic Signorini problems, Functional a posteriori error estimates for the parabolic obstacle problem, Hybridization and stabilization for \textit{hp}-finite element methods, Pointwise a posteriori error analysis of quadratic finite element method for the elliptic obstacle problem, Bubbles enriched quadratic finite element method for the 3D-elliptic obstacle problem, All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable, Discontinuous Galerkin methods for a contact problem with Tresca friction arising in linear elasticity, A posteriori error control and adaptivity of \(hp\)-finite elements for mixed and mixed-hybrid methods, A posteriori error estimates of virtual element method for a simplified friction problem, A novel hierarchial error estimate for elliptic obstacle problems, Adaptive finite element methods for a fourth order obstacle problem and a state constrained optimal control problem, An A Posteriori Analysis of $C^0$ Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates, Efficient and reliable hierarchical error estimates for an elliptic obstacle problem, Effective postprocessing for equilibration a posteriori error estimators, Mesh and model adaptivity for frictional contact problems, Hierarchical error estimates for the energy functional in obstacle problems, Efficient Discrete Lagrange Multipliers in three first-order finite element discretizations for the A Posteriori Error Control in an Obstacle Problem, Supremum-norm a posteriori error control of quadratic discontinuous Galerkin methods for the obstacle problem, Goal-oriented error control in adaptive mixed FEM for Signorini's problem, A posteriori error estimates of \(hp\)-adaptive IPDG-FEM for elliptic obstacle problems, A posteriori error estimates for discontinuous Galerkin methods of obstacle problems, Convergence analysis of a conforming adaptive finite element method for an obstacle problem, Inhomogeneous Dirichlet boundary condition in the \textit{a posteriori} error control of the obstacle problem, A posteriori error estimates of discontinuous Galerkin methods for the Signorini problem, A posteriori error estimator competition for conforming obstacle problems, Adaptive Finite Element Solution of Variational Inequalities with Application in Contact Problems, Numerical solution of a contact problem with unilateral constraint and history-dependent penetration, Convergence of adaptive FEM for some elliptic obstacle problem, Mimetic finite differences for nonlinear and control problems, Biorthogonal basis functions in \(hp\)-adaptive FEM for elliptic obstacle problems, A posteriori error control of \(hp\)-finite elements for variational inequalities of the first and second kind, Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis, Ten remarks on nonconvex minimisation for phase transition simulations, First-order least-squares method for the obstacle problem, A C ⁰ interior penalty method for a fourth-order variational inequality of the second kind, Higher order FEM for the obstacle problem of the \(p\)-Laplacian -- a variational inequality approach, NCP Function--Based Dual Weighted Residual Error Estimators for Signorini's Problem, Efficient and reliable hierarchical error estimates for the discretization error of elliptic obstacle problems, Convergence analysis of symmetric dual-wind discontinuous Galerkin approximation methods for the obstacle problem, Higher order mixed FEM for the obstacle problem of the \(p\)-Laplace equation using biorthogonal systems, A posteriori FE error control for p-Laplacian by gradient recovery in quasi-norm, An efficient and reliable residual-type a posteriori error estimator for the Signorini problem, A posteriori error estimators for obstacle problems -- another look, A Posteriori Estimator for the Adaptive Solution of a Quasi-Static Fracture Phase-Field Model with Irreversibility Constraints, A posteriori error control of discontinuous Galerkin methods for elliptic obstacle problems, Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods

Uses Software

• na14

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Inhomogeneous Dirichlet conditions in a priori and a posteriori finite element error analysis
• Averaging techniques for reliable a posteriori FE error control in elastoplasticity with hardening
• Weighted error estimates for finite element solutions of variational inequalities
• Remarks around 50 lines of Matlab: short finite element implementation
• Residual type a posteriori error estimates for elliptic obstacle problems
• Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems
• A posteriori error control in low-order finite element discretisations of incompressible stationary flow problems
• Positivity preserving finite element approximation
• On the Finite Element Approximation of an Elliptic Variational Inequality Arising from an Implicit Time Discretization of the Stefan Problem
• Error Estimates for the Approximation of a Class of Variational Inequalities
• Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part I: Low order conforming, nonconforming, and mixed FEM
• Each averaging technique yields reliable a posteriori error control in FEM on unstructured grids. Part II: Higher order FEM
• All first-order averaging techniques for a posteriori finite element error control on unstructured grids are efficient and reliable
• Quasi-Interpolation and A Posteriori Error Analysis in Finite Element Methods
• Averaging technique for FE -- a posteriori error control in elasticity. I: Conforming FEM