Mrs. Mallard's grieving process at the beginning of the story is essentially a textbook case: shock, grief, and acceptance. The story's heart, of course, are the additional circumstances that alter the process for Mrs. Mallard.
When Mrs. Mallard hears of her husband's death, she reacts as we would expect:
She wept at once, with sudden wild abandonment. . . . When the storm of grief had spent itself she went away to her room alone.
There is nothing in her initial reaction that surprises us. The fact that she grieved with "sudden wild abandonment," however, might seem odd for a woman of that era and station of life, but not surprising.
After the initial shock, which, fortunately, does not trigger a heart attack in her weak heart, Mrs. Mallard goes upstairs to sit in her bedroom and begins the acceptance stage. After sitting and seeing "new spring life," and feeling a "delicious breath of rain," hearing singing in the distance and birds "twittering in the eaves," she begins to sense
something coming to her. . . .creeping out of the sky, reaching toward her through the sounds, the scents, the color that filled the air.
Of course, her reaction to this as-yet undefined emotion is to "beat it back with her will," primarily because the emotion that is growing within her is, to put it in modern words, not politically correct for a newly-widowed woman.
Mrs. Mallard expresses this new emotion, a completely new sense of herself, in the words "'free, free, free!'" She has discovered, to her own surprise, that Brently Mallard's death has left her free of the repression of marriage and, more important, given her a life "that would belong to her absolutely." In fact, when she walks downstairs with this new, wonderful sense of freedom, she "carried herself unwittingly like a goddess of Victory." Even her body is expressing the sense of freedom and self-assertion that she believes is hers for the rest of her life.
At this point, she has gone through the grieving process--very short, I'll admit--and achieved the full revelation of her new life. Unfortunately, a new grieving process begins when Brently Mallard walks through the door, but the process begins and ends with her death, attributed ironically to "joy."