Generalized finite element solution to one-dimensional flux problems

A finite element numerical solution to the general one-dimensional flow equation is derived in a form that provides a convenient and general means to simulate a wide variety of one-dimensional flow techniques of interest to biological scientists, e.g., ultracentrifugation, electrophoresis, chromatography, etc. Diverse physical models defined in terms of column geometry, solute interactions, and the dependence of transport parameters on column position, time, or concentrations of one or more solutes, can be accommodated. A particularly useful aspect of the formulation is that a wide variety of boundary conditions can be simply applied to the end result, without rederivation of the solution for each new case. The numerical solution is expressed as matrix equations that are sufficiently general so that incorporation of particular models can be effected by substitution of appropriate quantities into the final result.