I have the impression, from very different resources and talks with researches, that there is a growing demand for high precision computations in numerical partial differential equations. Here, high precision means more precision than just the standard 64bit double precision.

I wonder about the state of the art of this topic. By way of comparision, there are communitites in numerical PDE which specifically target, e.g., multicore methods, large-scale parallelization or GPU-computing. I wonder whether a similar community is exists or is growing for high precision methods in numerical PDE, and I would be particulary interested (and this is the actual point of the question) in introductory or survey papers on high precision, which also provide an impression of the actual relevance of the topic.