This variational formulation does not take into account the embedded domain. Contrarily
to step-60, we do not enforce strongly the constraints of $\textbf{u}$ on $\Gamma$,
-but enforce them weakly.
+but enforce them weakly.
The analysis of this weak imposition of the boundary condition depends on the spacedim-dimensional measure
of $\Gamma$. We discuss both scenario.
@f{eqnarray*}
(\nabla \textbf{v}, \nabla \textbf{u})_{\Omega} + (\nabla \cdot \textbf{v}, p)_{\Omega}
- + (q, \nabla \cdot \textbf{u})_{\Omega}
- + \beta_1 (\textbf{v}},\textbf{u})_{\Gamma} &=&
+ + (q, \nabla \cdot \textbf{u})_{\Omega}
+ + \beta_1 (\textbf{v}},\textbf{u})_{\Gamma} &=&
\beta_1 (\textbf{v},\textbf{g})_{\Gamma}
@f}
+ (q, \nabla \cdot \textbf{u})_{\Omega}
+ \beta_1 (\textbf{v}},\textbf{u})_{\Gamma}
- \beta_2 (\nabla\textbf{v},\nabla \textbf{u})_{\Gamma}
- &=&
+ &=&
\beta_1 (\textbf{v},\textbf{g})_{\Gamma}
@f}
set Velocity degree = 2
set Viscosity = 1
subsection Angular velocity
- set Function constants =
+ set Function constants =
set Function expression = t < .5 ? 5 : -5
set Variable names = x,y,t
end
set Particle grid generator arguments = 0.3, 0.3: 0.1: false
end
subsection Right hand side
- set Function constants =
+ set Function constants =
set Function expression = 0; 0; 0
set Variable names = x,y,t
end
set Velocity degree = 2
set Viscosity = 1
subsection Angular velocity
- set Function constants =
+ set Function constants =
set Function expression = t < .5 ? 5 : -5
set Variable names = x,y,t
end
set Particle grid generator arguments = 0.3, 0.3: 0.1: false
end
subsection Right hand side
- set Function constants =
+ set Function constants =
set Function expression = 0; 0; 0
set Variable names = x,y,t
end