  We study the problem of approximation of solutions of the Skorokhod problem
and reflecting stochastic differential equations (SDEs) with jumps by sequences
of solutions of equations with penalization terms. Applications to discrete
approximation of weak and strong solutions of reflecting SDEs are given. Our
proofs are based on new estimates for solutions of equations with penalization
terms and the theory of convergence in the Jakubowski $S$-topology.
