A posteriori error estimator and h-adaptive finite element method for diffusion-advection-reaction problems

2014 ◽  
pp. 329-337
Author(s):  
O Ostapov ◽  
O Vovk ◽  
H Shynkarenko
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Posteriori Error ◽  
Adaptive Finite Element Method ◽  
Error Estimator ◽  
Adaptive Finite Element ◽  
A Posteriori ◽  
A Posteriori Error Estimator ◽  
Posteriori Error Estimator ◽  
A Posteriori Error

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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