least square FEM approximation of div-curl system
 

Hi All,

I am trying to solve a div-curl system i.e. div.V = f and curl V = 0 in omega with V.n = 0, (where V = u i + v j) as the boundary condition using least square finite element method. My domain is a 1X1 square with lower left corner as origin. I am using bilinear quadrilaterals. I am using 100 elements or 121 nodes ie 11X11 mesh. I have derived expressions for element stiffness matrices and i think they are correct.

my questions are

1. can any one point out some references (an engineer can easily understand) so that I can verify my derivations. I have looked at Jiang's book, but I need something more lucid.

2. can any body point out any literature for enforcing boundary conditions in finite elements. I want to enforce V.n = 0 very accurately.For eg. on lower boundary (y=0) it V.n = 0 means v =0. However in the solution I find that the v is small (O~1e-4), which is not acceptable.

Thanks, Abhijit