From what I understand, Mount Everest grows about 2.4 inches per year. I am trying to create an area of land that grows very often, often around 1 inch per day. As I'm not very good with plate tectonics, I was wondering what would be required to have that happen, and if it is even possible. I am planning on having that area of land be very unstable and unwelcoming, with lava flows very often, common earthquakes, rockfall, and the like. Ideally, whatever thing that causes the growth to happen would be relatively lethal.
Newly forming cinder and spatter cones or magma domes in stratovolcanoes (like Mt. Saint Helens) can grow this rapidly or even more so, though they generally do so for only a matter of a few weeks to a few years continuously, rather than for centuries.
Paracutin, a Mexican volcano that erupted out of a farmer's field, Surtsey, a historically new volcanic island near Iceland, and a few other examples in historic times have shown growth at or above this rate, for a matter of years -- but then they became dormant and stopped growing for a period of time. It's common, however, for such volcanoes to become active again after a period of dormancy, and if the magma is of the right composition, to continue adding height with each eruptive cycle. California's Mount Lassen is another example, and I'm sure there are others in the Andes (though I don't recall their names).