Residual-based a posteriori error estimator for the mixed finite element approximation of the biharmonic equation

2011 ◽  
Vol 27 (2) ◽  
pp. 315-328 ◽  
Author(s):  
Thirupathi Gudi
Keyword(s):  
Biharmonic Equation ◽  
Mixed Finite Element ◽  
Finite Element Approximation ◽  
Posteriori Error ◽  
Error Estimator ◽  
Element Approximation ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

An adaptive edge element approximation of a quasilinear H(curl)-elliptic problem

2020 ◽  
pp. 1-28
Author(s):  
Yifeng Xu ◽  
Irwin Yousept ◽  
Jun Zou
Keyword(s):  
Elliptic Problem ◽  
Posteriori Error ◽  
Error Estimator ◽  
Element Approximation ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error ◽  
Edge Element ◽  
Theoretical Results

An adaptive edge element method is designed to approximate a quasilinear [Formula: see text]-elliptic problem in magnetism, based on a residual-type a posteriori error estimator and general marking strategies. The error estimator is shown to be both reliable and efficient, and its resulting sequence of adaptively generated solutions converges strongly to the exact solution of the original quasilinear system. Numerical experiments are provided to verify the validity of the theoretical results.

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.

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