Extrapolation of the bilinear element approximation for the Poisson equation on anisotropic meshes

2007 ◽  
Vol 23 (5) ◽  
pp. 960-967 ◽  
Author(s):  
Qun Lin ◽  
Jia-fu Lin
Keyword(s):  
Poisson Equation ◽  
Element Approximation ◽  
Anisotropic Meshes ◽  
The Poisson Equation ◽  
Bilinear Element

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.

Lattice sums arising from the Poisson equation

2013 ◽  
Vol 46 (11) ◽  
pp. 115201 ◽  
Author(s):  
D H Bailey ◽  
J M Borwein ◽  
R E Crandall ◽  
I J Zucker
Keyword(s):  
Poisson Equation ◽  
Lattice Sums ◽  
The Poisson Equation
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