JOEL - Christ showed Himself to His disciples and let them touch Him and feel that he was a solid flesh and bone being. Then to emphasize the fact that he truely had a fully resurrected body, he "breathed on them" (John 29:22), and he ate some food to show them that He was real on the inside as well (Luke 24:42-43). Whether or not the food was actually digested is irrelevant. Remember that Jesus is God and can do whatever He wants.
Paul teaches that our present body will be changed to be like the glorious body of Christ (Phil. 3:20-21). So this could mean that after we die and are resurrected we will all probably be able to eat as well if we want, but because our bodies will no longer be aging and growing they will not need the nourishment. The resurrected body is tangible, but according to Joseph Smith, when the flesh is quickened by the Spirit there will be "spirit in their [veins] and not blood" (Teachings of the Prophet Joseph Smith, p. 367).
If there is no blood to take the nourishment to our cells then there is no need to eat food. There may not even be anything to eat in heaven. But what about during the Milennium while we are living as resurected beings on this earth? According to Orson Pratt:
In the testimony of our Savior to his Apostles, we learn that resurrected beings will eat and drink, for says he—"Ye that have followed me in the regeneration shall sit upon twelve thrones judging the twelve tribes of Israel, and ye shall eat and drink at my table." When will that be? During the Millennium, after the resurrection of those twelve Apostles, and when Jesus descends from heaven they will descend with him, and when he sits upon this throne in one of the apartments of the Temple, the twelve Apostles will sit upon their thrones, each one having a separate tribe of Israel over whom he will reign; and when dinner is ready, or supper, as the case may be, they will sit down at the Lord's table, and will eat and drink in his presence. We might say much more in relation to this matter, but if there is anything revealed to prove that immortality is dependent upon eating and drinking, the same as our mortal lives are dependent upon, I am not aware of it." (J of D. 16: 358-259)
So we probably won't need to eat food, but if there are occasions when we will be eating as resurected beings, how our bodies will process that food is a detail that has not been revealed to us yet.