Stokes problem fem I'm looking for a book or pdf to study the Stokes problem with finite elements method $\Delta u+\nabla p=f$ in $\Omega$ $\nabla\cdot u=0$ in $\Omega$ $+$ boundary conditions (example: $u=0$ on $\partial\Omega$. I'm interested in study the existence and uniqueness of the continuous and discrete problem, in particular the $\mathbb{P}_1/\mathbb{P}_0$ formulation ($\mathbb{P}_1$ for $u$ and $\mathbb{P}_0$ for $p$). Thanks!

The standard reference is _Mixed Finite Element Methods and Applications_ by Boffi-Brezzi-Fortin. The combination $P_1-P_0$ will not, in general, satisfy the discrete _inf-sup_ condition and therefore you must either stabilize the problem or use the so-called nonconforming $P_1-P_0$ approximation where the velocity is continuous only at the triangle edge midpoints (i.e., Crouzeix-Raviart shape functions).