Optimal error estimate of upwind scheme on Shishkin-type meshes for singularly perturbed parabolic problems with discontinuous convection coefficients

2010 ◽  
Vol 51 (2) ◽  
pp. 289-315 ◽  
Author(s):  
Kaushik Mukherjee ◽  
Srinivasan Natesan
1999 ◽  
Vol 09 (03) ◽  
pp. 395-414 ◽  
Author(s):  
C. BERNARDI ◽  
Y. MADAY

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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