Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems
From MaRDI portal
Publication:2706407
DOI10.1137/S0036142900370812zbMath0992.65073MaRDI QIDQ2706407
Publication date: 19 March 2001
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
elliptic variational inequalitiesnumerical integrationobstacle problemsa posteriori error estimatesadaptive finite element methodsresidual-type estimators
Numerical optimization and variational techniques (65K10) Variational inequalities (49J40) Newton-type methods (49M15)
Related Items
A reliable, efficient and localized error estimator for a discontinuous Galerkin method for the Signorini problem ⋮ Space adaptive finite element methods for dynamic Signorini problems ⋮ Pointwise a posteriori error analysis of quadratic finite element method for the elliptic obstacle problem ⋮ Adaptive optimal control of Signorini's problem ⋮ Bubbles enriched quadratic finite element method for the 3D-elliptic obstacle problem ⋮ Pointwise a posteriori error analysis of a finite element method for the Signorini problem ⋮ Discontinuous Galerkin methods for a contact problem with Tresca friction arising in linear elasticity ⋮ Constitutive-relation-error-based \textit{a posteriori} error bounds for a class of elliptic variational inequalities ⋮ Unnamed Item ⋮ A posteriori error estimates for parabolic variational inequalities ⋮ Multi-mesh adaptive finite element algorithms for constrained optimal control problems governed by semi-linear parabolic equations ⋮ A posteriori error estimates of virtual element method for a simplified friction problem ⋮ A novel hierarchial error estimate for elliptic obstacle problems ⋮ Mesh adaptivity for quasi‐static phase‐field fractures based on a residual‐type a posteriori error estimator ⋮ Mixed and Stabilized Finite Element Methods for the Obstacle Problem ⋮ Adaptive finite element methods for a fourth order obstacle problem and a state constrained optimal control problem ⋮ A posteriori error estimates for a compositional two-phase flow with nonlinear complementarity constraints ⋮ Adaptive quadratic finite element method for the unilateral contact problem ⋮ An A Posteriori Analysis of $C^0$ Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates ⋮ Residuala posteriori error estimators for contact problems in elasticity ⋮ A posteriorierror analysis for parabolic variational inequalities ⋮ Efficient and reliable hierarchical error estimates for an elliptic obstacle problem ⋮ 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 ⋮ Functional a posteriori error estimates for problems with nonlinear boundary conditions ⋮ 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 control for distributed elliptic optimal control problems with control constraints discretized by \(hp\)-finite elements ⋮ Adaptive finite element approximation for an elliptic optimal control problem with both pointwise and integral control constraints ⋮ A posteriori error estimates for discontinuous Galerkin methods of obstacle problems ⋮ Adaptive finite element methods for Cahn-Hilliard equations ⋮ 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 ⋮ Dual-weighted residual a posteriori error estimates for a penalized phase-field slit discontinuity problem ⋮ Space-time adaptive finite elements for nonlocal parabolic variational inequalities ⋮ A posteriori error estimator competition for conforming obstacle problems ⋮ Adaptive Finite Element Solution of Variational Inequalities with Application in Contact Problems ⋮ Error analysis of variational discretization solving temperature control problems ⋮ Convergence of adaptive FEM for some elliptic obstacle problem ⋮ Mimetic finite differences for nonlinear and control problems ⋮ A posteriori error analysis for the normal compliance problem ⋮ A posteriori error estimation and adaptive solution of elliptic variational inequalities of the second kind ⋮ Reliable, goal‐oriented postprocessing for FE‐discretizations ⋮ Averaging techniques yield reliable a posteriori finite element error control for obstacle problems ⋮ A posteriori error analysis for a class of integral equations and variational inequalities ⋮ A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities ⋮ Estimating the control error in discretized PDE-constrained optimization ⋮ A unified framework for high-order numerical discretizations of variational inequalities ⋮ 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 ⋮ 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 ⋮ Galerkin least squares finite element method for the obstacle problem ⋮ Error control in h- and hp-adaptive FEM for Signorini's problem ⋮ Higher order mixed FEM for the obstacle problem of the \(p\)-Laplace equation using biorthogonal systems ⋮ Adaptive inexact semismooth Newton methods for the contact problem between two membranes ⋮ Adaptive Optimal Control of the Obstacle Problem ⋮ An efficient and reliable residual-type a posteriori error estimator for the Signorini problem ⋮ A posteriori error estimations of residual type for Signorini's 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 ⋮ Adaptive Finite Elements for Optimally Controlled Elliptic Variational Inequalities of Obstacle Type ⋮ A posteriori error control of discontinuous Galerkin methods for elliptic obstacle problems ⋮ Two new approaches for solving elliptic obstacle problems using discontinuous Galerkin methods ⋮ A posteriori error estimates for optimal control problems constrained by convection-diffusion equations
