If at the time of execution of the will the testator fails to provide in the will for a living child of the testator solely because the testator believes the child to be dead, the child is entitled to receive a share in the estate as follows:

(1) If the testator had no other child living at the time the will was executed, an omitted child receives a share equal in value to that which the child would have received had the testator died intestate but only to the extent that any provision in the will to or for the benefit of the surviving parent of the omitted child is not thereby reduced; or

(2) If the will contains testamentary gifts to one or more other children of the testator, an omitted child is entitled to receive the share of the estate that the child would have received had the testator included all omitted children with the children to whom testamentary gifts were made under the will and had given an equal share to each child. To the extent feasible, the interest granted an omitted child must be of the same character, whether legal or equitable, present or future, as that left to the testator's other children under the will. In satisfying the share for the omitted child, the shares of the other children shall abate ratably, preserving to the maximum extent possible the testamentary plan adopted by the testator.