Analytical solutions of mass transport problems for error estimation of finite/infinite element methods

• Published in: Communications in numerical methods in engineering Vol. 11; no. 1; pp. 13 - 23
• Main Authors: Zhao, Chongbin, Steven, G. P.
• Format: Journal Article
• Language: English
• Published: Sussex John Wiley & Sons, Ltd 01.01.1995; Wiley
• Subjects: Computational techniques; error estimation; Exact sciences and technology; Finite-element and galerkin methods; mass transport problems; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Finite element method; Transport equation; Infinite medium; Partial differential equations; Error estimation; One dimensional model; Two dimensional model; Analytical solution; Discretization method; Mass transfer; Transients
• ISSN: 1069-8299; 1099-0887
• DOI: 10.1002/cnm.1640110104

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