ANALYTICAL SOLUTIONS OF MASS-TRANSPORT PROBLEMS FOR ERROR ESTIMATION OF FINITE INFINITE ELEMENT METHODS

In order to make an exact estimation of discretization error for finit e/infinite element methods, it is necessary to develop analytical solu tions for some transient mass transport problems in infinite media. Th ese transient mass transport problems may be viewed as the benchmark p roblems for the discretization error estimation of a new numerical met hod so that they generally have the following characteristics: (1) the ir initial and boundary conditions can be exactly modelled by the fini te/infinite element method; (2) their solutions can be rigorously expr essed in a closed form. In this paper, several of the aforementioned p roblems have been constructed and solved mathematically for transient mass transport problems in both 1D and 2D infinite media.