Assess students' ability to derive the weak (variational) formulation for a second‑order elliptic boundary value problem, identify appropriate Sobolev function spaces and boundary conditions, construct a Galerkin approximation (e.g. finite element basis), assemble the bilinear form and load vector, and apply basic well‑posedness and error estimates (Lax–Milgram, Céa's lemma) to justify convergence for a simple domain or element choice.