Look up your definition of digestion - it has a specific meaning. You will need something more sophisticated than 'breaking into smaller pieces' to get your head around this one.

Basically the stomach is like a big churning pot where food enters and is mized with strong hydrochloric acid secreted by the parietal cells into the lumen of the stomach. Furthermore, pepsin, a digestive enzyme activated by the acid, which helps to break proteins down into smaller polypeptide fragments for further digestion later, is secreted by chief/peptic cells in the stomach. Meanwhile the stomach has lots of bands of muscle in its wall, arranged into distinct layers, which help to provide a physical churning action to break down solid matter into smaller solids. This, coupled with the gastric secretions, helps to turn the lovely steak and chips you just ate into a thick liquid chyme. Little nutrition is actually abosroebd in the stomach, the majority of food and water is absorbed in the small intestine sections of the gut further on. However this is made much easier by the action sof the stomach, which basically starts the digestion process off. The action of breaking the foods down occurs outside of the cells of the stomach, within the stomach lumen itself, so is extracellular. Most generally speaking, because the food is quite large at first extracellular disgestion must occur in order for it to be broken down to allow it to be absorbed by cells later on in the gut, when it can then be sent to the liver for final processing. This is in comparison to, for example, the 'digestion' of bacteria by macropahges of the immune system (note is have used apostrophes because the macrophages don't really digest in the true sense of the word, they pahgocytose and kill). So, one word answer - extracellular.

Intracellular nor extracellular digestion occur in the human stomach. Intracellular digestion is digestion taking place inside of cells. However, most intracellular digestion takes place in uni-cellular protists which do not have a stomach. Instead, the cell engulfs the food particle by phagocytosis. The food particle enters through a coated vesicle and eventually attaches to a lysosome, which contains digestive enzymes which break down the food. Extracellular digestion is digestion that occurs OUTSIDE of cells. More complex organisms (i.e. humans) have extracellular digestion. I do not think you want an explanation of how this happens, plus my arms are very tired. So, to conclude and attempt to answer your question, intracellular nor extracellular digestion occur in the human stomach. I am not 100% sure if humans can go through intracellular and extracellular digestion. I don't think they can. I do know a hydra can.