Singular fibers of elliptic fibrations on normal $K3$ surfaces

We study singular fibers of elliptic fibrations on normal $K3$ surfaces. For a normal $K3$ surface $Y$ with minimal resolution $\nu \text{\hspace{0.17em}⁣}:X\to Y$, we describe singular fibers on $Y$ in terms of contractions of suitable ADE configurations of $(-2)$-curves in singular fibers on $X$. We determine ADE configurations occurring in singular fibers and describe fibers obtained after contraction. As a consequence, we obtain a description of singular fibers of elliptic fibrations on normal $K3$ surfaces.