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pjaap committed Oct 10, 2024
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Expand Up @@ -10,16 +10,16 @@ Solve the equation
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in $\Omega=(0,L)\times (0,H)$ with a homogeneous Neumann boundary condition
at $x=0$, an outflow boundary condition at $x=L$, a Dirichlet inflow
condition at $y=H$, and a homogeneous Dirichlet boundary condition
condition at $y=H$, and a homogeneous Dirichlet boundary condition
on part of $y=0$.
The analytical expression for the velocity field is $v(x,y)=(x^2,-2xy)$ in
The analytical expression for the velocity field is $v(x,y)=(x^2,-2xy)$ in
cartesian coordinates and $v(r,z)=(r^2,-3rz)$ in cylindrical coordinates, i.e.
where the system is solved on $\Omega$ to represent a solution on the solid
where the system is solved on $\Omega$ to represent a solution on the solid
of revolution arising from rotating $\Omega$ around $x=0$.
We compute the solution $u$ in both coordinate systems where $v$ is given
as an analytical expression and as a finite element interpolation onto
as an analytical expression and as a finite element interpolation onto
the grid of $\Omega$.
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