ABSTRACT
This chapter shows that the convergence rate of the modified method of characteristics (MMOC) depends on more than the approximation properties of the underlying function space. The finite element MMOC is a procedure for computing approximate solutions of advection-diffusion problems. Although it has the flavor of a Galerkin method, it has definite theoretical and experimental advantages over Galerkin methods in advection-dominated situations. In the context of a very simple model problem, it is shown that the convergence rate is the same for two modified method of characteristics schemes, one built on piecewise linear functions and the other built on piecewise quadratic functions.
