In order to reduce the numerical diffusion error of the convey-diffuse equation,the concept of concentration on cross section is introduced to calculate the mean concentration of river sections,and a new finite control volume method is put forward based on the incomplete mixing pattern.

This paper systematically studies the finite-element method of solving the Galerkin variation problem of the transport equation in well-logging condition and developed a finite-element mesh program which can be used in 2-dimension and 3-dimension well-logging domain.

The transport equation of air age is derived based on tracer gas technique.

In the frame of multigroup P_1 approximation the neutron transport equation is soluted by using finite-element method and the two-dimentional finite-element code FEMLOG is devel- oped for the numerical simulation of neutron well-logging.

In the first one,our aim is to prove the existence of a flow of measurable maps associated to a vector field belonging to a Sobolev space;to this end,we discuss the link with transport equations and continuity equations.