Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Adaptive multilevel methods for obstacle problems
SIAM Journal on Numerical Analysis
Adaptive Finite Elements for Elastic Bodies in Contact
SIAM Journal on Scientific Computing
Efficient and Reliable A Posteriori Error Estimators for Elliptic Obstacle Problems
SIAM Journal on Numerical Analysis
Journal of Scientific Computing
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Fully Localized A posteriori Error Estimators and Barrier Sets for Contact Problems
SIAM Journal on Numerical Analysis
Robust A Posteriori Error Estimation for Nonconforming Finite Element Approximation
SIAM Journal on Numerical Analysis
Computational Methods for Option Pricing (Frontiers in Applied Mathematics) (Frontiers in Applied Mathematics 30)
A posteriori error estimations of residual type for Signorini's problem
Numerische Mathematik
A posteriori error estimators for obstacle problems – another look
Numerische Mathematik
An a Posteriori Error Estimator for Two-Body Contact Problems on Non-Matching Meshes
Journal of Scientific Computing
A posteriori estimators for obstacle problems by the hypercircle method
Computing and Visualization in Science
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation Based on Potential and Flux Reconstruction for the Heat Equation
SIAM Journal on Numerical Analysis
Different a posteriori error estimators and indicators for contact problems
Mathematical and Computer Modelling: An International Journal
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In this paper, we consider a posteriori error estimators for obstacle problems. The variational inequality is reformulated as a mixed problem in terms of a discrete nodewise defined but variationally consistent Lagrange multiplier. Locally defined equilibrated fluxes and an $H(\mathrm{div})$-conforming lifting define our estimator. To obtain a better local upper bound for the estimator, we introduce a different elementwise defined Lagrange multiplier. Although the upper and lower bounds are established for affine obstacles, we present generalizations to nonsmooth obstacles and to nonmatching meshes. Different numerical examples show the efficiency and reliability of our estimator. Due to its flexible construction principle and abstract framework, it can be also applied as an error indicator to more complex obstacle problems such as, e.g., American option pricing in financial mathematics.