The continuous adjoint approach applied to the stabilized finite-element formulation of the incompressible Navier-Stokes equations

2019 ◽  
Author(s):  
Bart Janssens ◽  
Pierre Vandenschrick ◽  
Kasper Stevens ◽  
Giacomo Alessi
Keyword(s):  
Finite Element ◽  
Stokes Equations ◽  
Finite Element Formulation ◽  
Navier Stokes ◽  
Element Formulation ◽  
Navier Stokes Equations ◽  
Stabilized Finite Element ◽  
Adjoint Approach ◽  
Continuous Adjoint

On the Finite Element Formulation of Navier–Stokes Equations

1973 ◽  
Vol 2 (4) ◽  
pp. 205-208
Author(s):  
E. Bilgen ◽  
J.J.M. Too
Keyword(s):  
Finite Element ◽  
Variational Formulation ◽  
Stokes Equations ◽  
Finite Element Formulation ◽  
Navier Stokes ◽  
Simple Problem ◽  
Element Formulation ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Pressure Fields

A variational formulation of the Navier-Stokes equation for steady flow of an incompressible fluid is presented and the limitations of the resulting equation are discussed. The finite element formulation based on the minimizing of functionals of the velocity and pressure fields is presented and a simple problem is treated to illustrate the method.

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