finite element in two layers

What should the finite element Matlab code look like in order to solve such a PDE in two layers?

[Torsten]

You have 7 equations in 6 unknowns. Thus one of the equations must be superfluous - most probably because pressure is missing as a solution variable.

[ahmed]

This is true so i updated the file now it has 6 on 6.

[Torsten]

Since you have second-order PDEs for U and V, only one transmission condition for U at y = 0.8 (U1 = U2) is not sufficient. As for theta, you need a second condition connecting dU1/dy and dU2/dy.

And what is the domain on which you want to solve your equations ? What are the conditions on the outer boundaries ((x = 0, ymin <= y <= ymax) and (x = 1, ymin <= y <= ymax) and (0 <= x <= 1, y = ymin) and (0 <= x <= 1, y = ymax)) ?

Maybe you could also explain what the variables U, V and Theta mean and what you try to model.

[ahmed]

I'm attempting to modify the problem in the attachment, and I anticipate that the FEM in Matlab code will be an effective method for this geometry.