Assess students' ability to analyze convergence rates and derive a priori error estimates for the Galerkin finite element method applied to the Poisson problem: include formulation of the weak problem, proof of H1 (energy) error bounds via Céa's lemma and interpolation estimates, derivation of L2 error estimates using the Aubin–Nitsche duality argument with explicit regularity assumptions, and identification of algebraic rates for degree-k piecewise polynomial spaces on quasi-uniform meshes. Require statement of assumptions (regularity, mesh, approximation properties), clear derivations of O(h^k) in H1 and O(h^{k+1}) in L2 under standard conditions, and brief discussion of limitations and implications for practice.