Hi professor,
Much thanks for this discussion that help me find the bugs when I do an ALE problem, I first use tgv=-1 and forget to enforce the boundary condition to the off-diagonal block of the Jacobian matrix, the convergency of Newton iteration is very slow.
My method is to set tgv=1e30, not exact Dirichlet boundary condition but the results are acceptable and easy to do parallel computation, not needed to update varf or Mat. Another way I find is to zero-out the corresponding rows in the off-diagonal block by hand, as in this post https://community.freefem.org/t/preferred-way-to-construct-block-matrices-with-exact-dirichlet-bc-tgv-1/222/2.