Bringing together a decade's worth of research stimulated by Miller's original idea of moving finite elements, this important book discusses the interrelationship between the techniques and the theories regarding the method of characteristics, Hamilton's equations, the Legendre transformation, and grid equidistribution. Throughout, the important issues are cogently highlighted, cutting-edge research developments are detailed, and areas for future research are discussed. Students, teachers, and researchers in applied mathematics, numerical analysis, engineering, and the computational sciences will want to read this book.