What could be the best way to implement the roller constraint in finite element code, i.e. constraint of the type

$$\mathbf{u} \cdot \mathbf{n} = 0$$

I plan to enforce it in the weak sense by incorporating

$$\int_\Gamma \lambda \mathbf{u} \cdot \mathbf{n} \, dA$$

into the weak form. However, it needs to define the Lagrange multiplier at the node, which will increase the system size.

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    $\begingroup$ For what problem? The answer might be very different for, say, the Euler equations vs the Stokes equations. $\endgroup$ Aug 10, 2023 at 0:09
  • $\begingroup$ This type of constraint is usually implemented by performing a coordinate transformation at the roller node so that the direction n is along one of the coordinate axes. Then a zero constraint is applied in the usual way to that DOF. $\endgroup$ Aug 10, 2023 at 10:44
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    $\begingroup$ You might find scicomp.stackexchange.com/questions/36432/… useful $\endgroup$
    – NNN
    Aug 10, 2023 at 11:17
  • $\begingroup$ @BillGreene I'm looking for the roller constraint on a cylinder surface. I think nodal constraint does not work for that case. $\endgroup$
    – kstn
    Aug 10, 2023 at 20:54
  • 2
    $\begingroup$ Are you doing a linear or nonlinear analysis? If linear, just create a coordinate system with an axis normal to the surface and constrain that dof. $\endgroup$ Aug 10, 2023 at 22:08


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