scholarly journals Optimal error estimate of elliptic problems with Dirac sources for discontinuous and enriched Galerkin methods

2020 ◽  
Vol 150 ◽  
pp. 76-104 ◽  
Author(s):  
Woocheol Choi ◽  
Sanghyun Lee
Keyword(s):  
Error Estimate ◽  
Elliptic Problems ◽  
Optimal Error Estimate ◽  
Galerkin Methods ◽  
Optimal Error

UNIFORM INF–SUP CONDITIONS FOR THE SPECTRAL DISCRETIZATION OF THE STOKES PROBLEM

1999 ◽  
Vol 09 (03) ◽  
pp. 395-414 ◽  
Author(s):  
C. BERNARDI ◽  
Y. MADAY
Keyword(s):  
Error Estimate ◽  
Error Estimates ◽  
Best Approximation ◽  
Stokes Problem ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Discretization Parameter ◽  
The Best Approximation ◽  
Discrete Spaces ◽  
Spectral Discretization

In standard spectral discretizations of the Stokes problem, error estimates on the pressure are slightly less accurate than the best approximation estimates, since the constant of the Babuška–Brezzi inf–sup condition is not bounded independently of the discretization parameter. In this paper, we propose two possible discrete spaces for the pressure: for each of them, we prove a uniform inf–sup condition, which leads in particular to an optimal error estimate on the pressure.

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