  We prove existence and uniqueness of solutions of reflected backward
stochastic differential equations in time-dependent adapted and c\`adl\`ag
convex regions $\mathcal{D}=\{D_t;t\in[0,T]\}$. We also show that the solution
may be approximated by solutions of backward equations with reflection in
appropriately defined discretizations of $\mathcal{D}$ and by a modified
penalization method. The approximation results are new even in the
one-dimensional case.
