Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Adaptive multilevel methods for obstacle problems
SIAM Journal on Numerical Analysis
A posteriori error estimation and adaptive mesh-refinement techniques
ICCAM'92 Proceedings of the fifth international conference on Computational and applied mathematics
Adaptive Finite Elements for Elastic Bodies in Contact
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Posteriori Error Estimators for a Class of Variational Inequalities
Journal of Scientific Computing
A Posteriori Error Control of Finite Element Approximations for Coulomb's Frictional Contact
SIAM Journal on Scientific Computing
A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
SIAM Journal on Numerical Analysis
Error indicators for the mortar finite element discretization of the Laplace equation
Mathematics of Computation
Mixed finite element methods for unilateral problems: convergence analysis and numerical studies
Mathematics of Computation
Quadratic finite element methods for unilateral contact problems
Applied Numerical Mathematics
Hybrid finite element methods for the Signorini problem
Mathematics of Computation
Applied Numerical Mathematics
Fully Localized A posteriori Error Estimators and Barrier Sets for Contact Problems
SIAM Journal on Numerical Analysis
An Optimal A Priori Error Estimate for Nonlinear Multibody Contact Problems
SIAM Journal on Numerical Analysis
A posteriori error estimations of residual type for Signorini's problem
Numerische Mathematik
A posteriori error estimators for obstacle problems – another look
Numerische Mathematik
Different a posteriori error estimators and indicators for contact problems
Mathematical and Computer Modelling: An International Journal
A posteriori error analysis of a domain decomposition algorithm for unilateral contact problem
Computers and Structures
A Posteriori Error Estimator for Obstacle Problems
SIAM Journal on Scientific Computing
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A posteriori error estimates for two-body contact problems are established. The discretization is based on mortar finite elements with dual Lagrange multipliers. To define locally the error estimator, Arnold---Winther elements for the stress and equilibrated fluxes for the surface traction are used. Using the Lagrange multiplier on the contact zone as Neumann boundary conditions, equilibrated fluxes can be locally computed. In terms of these fluxes, we define on each element a symmetric and globally H(div)-conforming approximation for the stress. Upper and lower bounds for the discretization error in the energy norm are provided. In contrast to many other approaches, the constant in the upper bound is, up to higher order terms, equal to one. Numerical examples illustrate the reliability and efficiency of the estimator.