Uniformly Convergent Cubic Nonconforming Element For Darcy–Stokes Problem

2017 ◽  
Vol 72 (1) ◽  
pp. 231-251 ◽  
Author(s):  
Shao-chun Chen ◽  
Li-na Dong ◽  
Ji-kun Zhao
Keyword(s):  
Stokes Problem ◽  
Nonconforming Element ◽  
Uniformly Convergent

Uniformly convergent H(div)-conforming rectangular elements for Darcy-Stokes problem

2013 ◽  
Vol 56 (12) ◽  
pp. 2723-2736 ◽  
Author(s):  
ShaoChun Chen ◽  
LiNa Dong ◽  
ZhongHua Qiao
Keyword(s):  
Stokes Problem ◽  
Uniformly Convergent

scholarly journals A Framework for Approximation of the Stokes Equations in an Axisymmetric Domain

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Niklas Ericsson
Keyword(s):  
Fourier Expansion ◽  
Stokes Equations ◽  
Stokes Problem ◽  
Three Dimensional ◽  
Countable Family ◽  
Angular Variable ◽  
Two Dimensional ◽  
Sobolev Norms ◽  
Well Posed ◽  
Variational Formulations

Abstract We develop a framework for solving the stationary, incompressible Stokes equations in an axisymmetric domain. By means of Fourier expansion with respect to the angular variable, the three-dimensional Stokes problem is reduced to an equivalent, countable family of decoupled two-dimensional problems. By using decomposition of three-dimensional Sobolev norms, we derive natural variational spaces for the two-dimensional problems, and show that the variational formulations are well-posed. We analyze the error due to Fourier truncation and conclude that, for data that are sufficiently regular, it suffices to solve a small number of two-dimensional problems.

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