Two-Grid Finite Element Methods for the Steady Navier-Stokes/Darcy Model

2016 ◽  
Vol 6 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Jing Zhao ◽  
Tong Zhang
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Navier Stokes ◽  
Optimal Error Estimates ◽  
Numerical Computations ◽  
Optimal Error ◽  
Darcy Model ◽  
Efficiency And Effectiveness ◽  
Grid Algorithm

AbstractTwo-grid finite element methods for the steady Navier-Stokes/Darcy model are considered. Stability and optimal error estimates in the H1-norm for velocity and piezometric approximations and the L2-norm for pressure are established under mesh sizes satisfying h = H2. A modified decoupled and linearised two-grid algorithm is developed, together with some associated optimal error estimates. Our method and results extend and improve an earlier investigation, and some numerical computations illustrate the efficiency and effectiveness of the new algorithm.

scholarly journals Numerical analysis for a chemotaxis-Navier-Stokes system

2020 ◽  
Author(s):  
Abelardo Duarte-Rodríguez ◽  
María A. Rodríguez-Bellido ◽  
Diego A. Rueda-Gómez ◽  
Élder J. Villamizar-Roa
Keyword(s):  
Finite Element ◽  
Error Estimates ◽  
Numerical Scheme ◽  
Stokes System ◽  
Equivalent Model ◽  
Navier Stokes ◽  
Optimal Error Estimates ◽  
Element Approximation ◽  
Optimal Error ◽  
Uniform Estimates

In this paper we develop a numerical scheme for approximating a $d$-dimensional chemotaxis-Navier-Stokes system, $d=2,3$, modeling cellular swimming in incompressible fluids. This model describes the chemotaxis-fluid interaction in cases where the chemical signal is consumed with a rate proportional to the amount of organisms. We construct numerical approximations based on the Finite Element method and analyze optimal error estimates and convergence towards regular solutions. In order to construct the numerical scheme, we use a splitting technique to deal with the chemo-attraction term in the cell-density equation, leading to introduce a new variable given by the gradient of the chemical concentration. Having the equivalent model, we consider a fully discrete Finite Element approximation which is  well-posed and mass-conservative. We obtain uniform estimates and analyze the convergence of the scheme. Finally, we present some numerical simulations to verify the good behavior of our scheme, as well as to check numerically the optimal error estimates proved in our theoretical analysis.

ERROR ANALYSIS OF MIXED-INTERPOLATED ELEMENTS FOR REISSNER-MINDLIN PLATES

1991 ◽  
Vol 01 (02) ◽  
pp. 125-151 ◽  
Author(s):  
FRANCO BREZZI ◽  
MICHEL FORTIN ◽  
ROLF STENBERG
Keyword(s):  
Finite Element ◽  
Error Analysis ◽  
Error Estimates ◽  
Finite Element Methods ◽  
Shear Force ◽  
New Method ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Linear Approximations

We give an error analysis for the recently introduced mixed-interpolated finite element methods for Reissner-Mindlin plates. Optimal error estimates, which are valid uniformly with respect to the thickness of the plate, are proven for the deflection, rotation and the shear force. In addition, the earlier families are augmented with a new method with linear approximations for the deflection and the rotation. We also introduce a simple postprocessing method by which an improved approximation for the deflection can be obtained.

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