Mitchell presents results that compare several techniques for the adaptive refinement of triangulations of piecewise linear functions used with finite element methods. He briefly describes each method, thus giving a nice survey of the current research in this area. He examines various procedures for dividing triangles and for indicating which triangles have the largest errors over a population of test problems. Numerical experiments compare the performance of the methods based on the achieved accuracy relative to the number of vertices. The author presents pros and cons of the methods studied and recommends when to use each. This paper is well written and very readable.