Inhomogeneous Dirichlet bounday conditions with Raviart-Thomas (RT) elements

[Sumedh Yadav]

Hello,
I intend to use RT elements for my fluid flow problem and the test case (2D) is shear flow. Consequently the I need to apply constant shear/sliding velocity (u_x = shear_velocity, u_y = 0) at top and bottom boundaries and velocities of form u_y = 0, u_x = y*shear_velocity for the right and left boundaries. I came across the function VectorTools::project_boundary_values_div_conforming () that helps to apply inhomogeneous dirichlet bcs but only in the normal direction (normal to boundary face), but what I also intend to do is apply dirichlet bcs for non-normal component (i.e. for u_x at top and bottom boundary) for RT elements. Is there any way out?

Please note that we can not simply use VectorTools::interpolate_boundary_values() for RT elements. Previous discussion on this topic - here.

[Daniel Arndt]

Sumedh,

I intend to use RT elements for my fluid flow problem and the test case (2D) is shear flow. Consequently the I need to apply constant shear/sliding velocity (u_x = shear_velocity, u_y = 0) at top and bottom boundaries and velocities of form u_y = 0, u_x = y*shear_velocity for the right and left boundaries. I came across the function VectorTools::project_boundary_values_div_conforming () that helps to apply inhomogeneous dirichlet bcs but only in the normal direction (normal to boundary face), but what I also intend to do is apply dirichlet bcs for non-normal component (i.e. for u_x at top and bottom boundary) for RT elements. Is there any way out?

RT elements are non-conforming and consequently you most likely want to use a DG formulation. In particular, you would normally prescribe Dirichlet boundary values in a weak sense.
You might want to have a look at the DG formulation of the Poisson problem in step-39.

Best,
Daniel