A generalized nodal finite element formalism for discrete ordinates equations in slab geometry part I: Theory in the continuous moment case

A generalized nodal finite element formalism is presented, which covers virtually all known finite difference approximations to the discrete ordinates equations in slab geometry. This paper (Part I) presents the theory of the so-called “continuous moment methods”, which include such well-known methods as the “diamond difference” and the “characteristic” schemes. In a second paper (hereafter referred to as Part II), we shall present the theory of the “discontinuous moment methods”, consisting in particular of the “linear discontinuous” scheme as well as of an entire new class of schemes. Corresponding numerical results are available for all these schemes and will be presented in a third paper (Part III).