F12 Finite Element Approximations to the Poisson Equation and the Advection Equation by Variant Hermite Triangular Elements of 3rd Order

2006 ◽  
Vol 2006.19 (0) ◽  
pp. 15-16
Author(s):  
Yuki UEDA ◽  
Masahisa TABATA
Keyword(s):  
Finite Element ◽  
Poisson Equation ◽  
Advection Equation ◽  
Finite Element Approximations ◽  
The Poisson Equation ◽  
Triangular Elements

scholarly journals A Note on Multilevel Based Error Estimation

2016 ◽  
Vol 16 (3) ◽  
pp. 447-458 ◽  
Author(s):  
Helmut Harbrecht ◽  
Reinhold Schneider
Keyword(s):  
Finite Element ◽  
Poisson Equation ◽  
Error Estimation ◽  
Finite Element Approximation ◽  
Error Estimator ◽  
Element Approximation ◽  
Finite Element Approximations ◽  
The Poisson Equation ◽  
Galerkin Solution ◽  
Edge Based

AbstractBy employing the infinite multilevel representation of the residual, we derive computable bounds to estimate the distance of finite element approximations to the solution of the Poisson equation. If the finite element approximation is a Galerkin solution, the derived error estimator coincides with the standard element and edge based estimator. If Galerkin orthogonality is not satisfied, then the discrete residual additionally appears in terms of the BPX preconditioner. As a by-product of the present analysis, conditions are derived such that the hierarchical error estimation is reliable and efficient.

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