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.

Solvability of one nonlocal Dirichlet problem for the Poisson equation

2019 ◽  
Vol 50 (1) ◽  
pp. 67-88
Author(s):  
Batirkhan Turmetov ◽  
Valery Karachik
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
The Poisson Equation

scholarly journals Application of p-Multigrid to Discontinuous Galerkin Formulations of the Poisson Equation

AIAA Journal ◽  
2006 ◽  
Vol 44 (3) ◽  
pp. 566-575 ◽  
Author(s):  
Brian T. Helenbrook ◽  
H. L. Atkins
Keyword(s):  
Discontinuous Galerkin ◽  
Poisson Equation ◽  
The Poisson Equation

scholarly journals Homogenization of the Poisson equation with Dirichlet conditions in random perforated domains

2015 ◽  
Vol 275 ◽  
pp. 375-381 ◽  
Author(s):  
Carmen Calvo-Jurado ◽  
Juan Casado-Díaz ◽  
Manuel Luna-Laynez
Keyword(s):  
Poisson Equation ◽  
Perforated Domains ◽  
Dirichlet Conditions ◽  
The Poisson Equation

A spectral Monte Carlo method for the Poisson equation

2004 ◽  
Vol 10 (3-4) ◽  
Author(s):  
Emmanuel Gobet ◽  
Sylvain Maire
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Poisson Equation ◽  
The Poisson Equation

Convergence and complexity of arbitrary order adaptive mixed element methods for the Poisson equation

2012 ◽  
Vol 55 (5) ◽  
pp. 1083-1098 ◽  
Author(s):  
JianGuo Huang ◽  
YiFeng Xu
Keyword(s):  
Poisson Equation ◽  
Arbitrary Order ◽  
The Poisson Equation ◽  
Mixed Element

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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