For $f\in L^2(\mathbb{R}^d)$ with $d\geq 1$, by Riesz representation theorem we know that there exists unique $u\in H^1(\mathbb{R}^d)$ such that $$<u,\phi>=<f,\phi>,\quad \forall \phi \in H^1(\mathbb{R}^d)$$ then $u$ solves the equation $$-\Delta u +u =f$$ in the distribution sense.
My question is: how to obtain the regularity of solution $u$, i.e. how to prove that $u\in H^2(\mathbb{R}^d)$?.