Concepts of an adaptive hierarchical finite element code
IMPACT of Computing in Science and Engineering
A posteriori error estimates based on hierarchical bases
SIAM Journal on Numerical Analysis
Adaptive multilevel methods for obstacle problems
SIAM Journal on Numerical Analysis
A convergent adaptive algorithm for Poisson's equation
SIAM Journal on Numerical Analysis
A posteriori error estimates for elliptic problems in two and three space dimensions
SIAM Journal on Numerical Analysis
Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems
SIAM Journal on Numerical Analysis
A Posteriori Error Estimators for Regularized Total Variation of Characteristic Functions
SIAM Journal on Numerical Analysis
Fully Localized A posteriori Error Estimators and Barrier Sets for Contact Problems
SIAM Journal on Numerical Analysis
A posteriori error estimators for obstacle problems – another look
Numerische Mathematik
A Unilaterally Constrained Quadratic Minimization with Adaptive Finite Elements
SIAM Journal on Optimization
A posteriori estimators for obstacle problems by the hypercircle method
Computing and Visualization in Science
Efficient and reliable hierarchical error estimates for an elliptic obstacle problem
Applied Numerical Mathematics
Hierarchical error estimates for the energy functional in obstacle problems
Numerische Mathematik
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We present and analyze a novel hierarchical a posteriori error estimate for elliptic obstacle problems. The main result is that the energy norm of the finite element approximate error is, up to some extra oscillation term, equivalent to an appropriate hierarchical estimator. The proof is based upon some new observations on efficiency and some technical tools deriving from a previous work (Zou et al. in Numer. Math. 117:653---677, 2011). Moreover, we present an equivalence between the energy norm and the energy functional of the finite element approximate error. Several numerical experiments validate our theoretical findings.