scholarly journals Two-parameter anisotropic homogenization for a Dirichlet problem for the Poisson equation in an unbounded periodically perforated domain. A functional analytic approach

2018 ◽  
Vol 291 (8-9) ◽  
pp. 1310-1341 ◽  
Author(s):  
Massimo Lanza de Cristoforis ◽  
Paolo Musolino
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
Analytic Approach ◽  
Perforated Domain ◽  
The Poisson Equation ◽  
Two Parameter

scholarly journals A saturation property for the spectral-Galerkin approximation of a Dirichlet problem in a square

2019 ◽  
Vol 53 (3) ◽  
pp. 987-1003 ◽  
Author(s):  
Claudio Canuto ◽  
Ricardo H. Nochetto ◽  
Rob P. Stevenson ◽  
Marco Verani
Keyword(s):  
Dirichlet Problem ◽  
Poisson Equation ◽  
Galerkin Approximation ◽  
Error Reduction ◽  
Two Dimensional ◽  
Dirichlet Problems ◽  
Polynomial Degree ◽  
Unit Square ◽  
The Poisson Equation ◽  
Dimensional Unit

Both practice and analysis of p-FEMs and adaptive hp-FEMs raise the question what increment in the current polynomial degree p guarantees a p-independent reduction of the Galerkin error. We answer this question for the p-FEM in the simplified context of homogeneous Dirichlet problems for the Poisson equation in the two dimensional unit square with polynomial data of degree p. We show that an increment proportional to p yields a p-robust error reduction and provide computational evidence that a constant increment does not.

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