Fully discrete finite element method based on pressure stabilization for the transient Stokes equations

2012 ◽  
Vol 82 (8) ◽  
pp. 1496-1515 ◽  
Author(s):  
Tong Zhang ◽  
Yinnian He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stokes Equations ◽  
Fully Discrete ◽  
Pressure Stabilization ◽  
Discrete Finite Element ◽  
Element Method

scholarly journals Error analysis of a fully discrete finite element method for incompressible flow with variable density

2020 ◽  
Author(s):  
Wentao Cai ◽  
Buyang Li ◽  
Ying Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Coupled System ◽  
Variable Density ◽  
Spatial Error ◽  
Fully Discrete ◽  
Stabilized Finite Element Method ◽  
Element Method

An error estimate is presented for a fully discrete, linearized and stabilized finite element method for solving the coupled system of nonlinear hyperbolic and parabolic equations describing incompressible flow with variable density. In particular, the error of the numerical solution is split into the temporal and spatial components, separately. The temporal error is estimated by applying discrete maximal L^p-regularity of time-dependent Stokes equations, and the spatial error is estimated by using energy techniques based on the uniform regularity of the solutions given by semi-discretization in time.

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