Spectral-Galerkin approximation and optimal error estimate for biharmonic eigenvalue problems in circular/spherical/elliptical domains

2019 ◽  
Vol 84 (2) ◽  
pp. 427-455
Author(s):  
Jing An ◽  
Huiyuan Li ◽  
Zhimin Zhang
Keyword(s):  
Error Estimate ◽  
Eigenvalue Problems ◽  
Galerkin Approximation ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Biharmonic Eigenvalue Problems

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.

scholarly journals A Discontinuous Finite Volume Method for the Darcy-Stokes Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Zhe Yin ◽  
Ziwen Jiang ◽  
Qiang Xu
Keyword(s):  
Error Estimate ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Optimal Error Estimate ◽  
Optimal Error ◽  
Numerical Examples ◽  
First Order ◽  
Theoretical Predictions ◽  
Volume Method

This paper proposes a discontinuous finite volume method for the Darcy-Stokes equations. An optimal error estimate for the approximation of velocity is obtained in a mesh-dependent norm. First-orderL2-error estimates are derived for the approximations of both velocity and pressure. Some numerical examples verifying the theoretical predictions are presented.

Sign in / Sign up

Export Citation Format

Share Document