Self-realization constitutes the thematic resolution of each of these stories.
For Celie the achievement of forgiveness, emotional maturity and a realization of self and personal strength mark her character's successful journey. This arc of her story is one that essentially begins at a low point and gradually rises in terms of her well-being, state of mind, actual situation and self-regard. Her children and sister return to her at the novel's end, completing her rise from abuse and powerlessness to self-acceptance, self-empowerment and fulfillment.
Nora's journey is quite different in its dynamic. Her story follows a more traditional dramatic arc as she experiences several "ups and downs" and anticipates a specific salvation via Helmer, which does not materialize. The crux of Nora's story is quite isolated then, occurring at the moment of confrontation when Helmer discovers Nora's secret (the loan to Krogstad, the forgery and the blackmail, etc.).
This narrative formula is distinctly different from the one that describes the growth of Celie's character. Nora exists in a more-or-less continuous state of anticipation and anxiety and, in her character's big moment, faces a crisis that forces her to change.
She does change as a result of the crisis and the nature of this change clearly resembles the one that Celie gradually undertakes. Nora asserts herself and asserts her rights to an identity of her own.
Helmer: Before anything else, you’re a wife and mother.
Nora: I don’t believe that any more. I believe that before anything else, I’m a human being, just as much a one as you are … or at least I’m going to turn myself into one.… I want to think everything out for myself and make my own decisions.
An obvious difference between Nora's story and Celie's is that Nora leaves her children in the end where Celie is re-united with hers. Yet, the self-realization and emotional maturity that each character achieves is similar.
Celie's transformation from a young passive girl, who is the object of violence and cruelty from her stepfather and her husband, into an independent woman with self-esteem is at the heart of The Color Purple. (eNotes)
Thematically we can say the same thing about Ibsen's play. However, we cannot say that the two stories are narratively parallel for the reasons stated above.