I have taken [-2,2]\times [-2,2] as domain with interface [-1,1]\times[-1,1]. But after solving in Free Fem++, I am getting a large error for pressure. Please look into it.
stokessquareinterface.edp (1.8 KB)
You are solving a problem with unknowns [ut1x,ut1y,pt1] in domain T1, and [ut2s,ut2y,pt2] in domain T2. There is no coupling in your problem since in your variational formulation there is no cross termm mixing [ut1x,ut1y,pt1] and [vt2x,vt2y,qt2], or [ut2x,ut2y,pt2] and [vt1x,vt1y,qt1]
As a consequence, your are solving two independent problems of stokes for [ut1x,ut1y,pt1] over T1, and Stokes for [ut2x,ut2y,pt2] on T2.
The boundary conditions you set are not satisfied by your “candidate solutions” [u1x,u1y,p1],
and [u2x,u2y,p2]. This is why you don’t get these candidate solutions.
For informatio, the boundary conditions set by your variational formulation are:
For [u2x,u2y,p2] :
u2x=0, u2y=0 on the external boundary,
(b_2 \\nabla u_2-p_2)N=0 on the internal boundary
For [u1x,u1y,p1]
(b_1\\nabla u_1-p_1)N=0 on the internal boundary