Guaranteed A Posteriori Error Estimator for Mixed Finite Element Methods of Linear Elasticity with Weak Stress Symmetry

2011 ◽  
Vol 49 (6) ◽  
pp. 2364-2385 ◽  
Author(s):  
Kwang-Yeon Kim
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Linear Elasticity ◽  
Mixed Finite Element ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

scholarly journals Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Xuehai Huang
Keyword(s):  
Finite Element ◽  
Mixed Finite Element ◽  
Posteriori Error ◽  
Error Estimator ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Bending Problems ◽  
Stabilized Mixed Finite Element

Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection inH1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument.

scholarly journals Residual-based a posteriori error estimation for hp-adaptive finite element methods for the Stokes equations

2019 ◽  
Vol 27 (4) ◽  
pp. 237-252
Author(s):  
Arezou Ghesmati ◽  
Wolfgang Bangerth ◽  
Bruno Turcksin
Keyword(s):  
Finite Element ◽  
Error Estimation ◽  
Posteriori Error ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
Posteriori Error Estimation ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

AbstractWe derive a residual-based a posteriori error estimator for the conforminghp-Adaptive Finite Element Method (hp-AFEM) for the steady state Stokes problem describing the slow motion of an incompressible fluid. This error estimator is obtained by extending the idea of a posteriori error estimation for the classicalh-version of AFEM. We also establish the reliability and efficiency of the error estimator. The proofs are based on the well-known Clément-type interpolation operator introduced in [27] in the context of thehp-AFEM. Numerical experiments show the performance of an adaptivehp-FEM algorithm using the proposed a posteriori error estimator.

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