A family of mixed finite elements for the elasticity problem
Numerische Mathematik
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
A posteriori error estimators for mixed finite element methods in linear elasticity
Numerische Mathematik
A Local A Posteriori Error Estimator Based on Equilibrated Fluxes
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
SIAM Journal on Numerical Analysis
A Posteriori Error Estimation for Lowest Order Raviart-Thomas Mixed Finite Elements
SIAM Journal on Scientific Computing
A framework for obtaining guaranteed error bounds for finite element approximations
Journal of Computational and Applied Mathematics
A Unified Analysis of Several Mixed Methods for Elasticity with Weak Stress Symmetry
Journal of Scientific Computing
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In this paper we propose an a posteriori error estimator for the mixed finite element methods of the linear elasticity problem with the symmetry condition weakly imposed on the stress tensor. The error estimator is constructed by making a proper decomposition of the stress error and using an argument similar to the hypercircle method. It is shown that the resulting estimator yields a guaranteed upper bound on the stress error which relies on computable upper bounds of the constants in the first and second Korn inequalities. We also establish the local lower bound by using the discrete Friedrichs inequality. Our approach is equivalent to the Helmholtz decomposition of the stress error but requires assumptions neither on the regularity of the solution nor the geometry of the domain. Numerical results are provided to illustrate the efficiency of our error estimator.