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Analytical solutions of mass transport problems for error estimation of finite/infinite element methods. (English) Zbl 0811.65073
Summary: In order to make an exact estimation of the 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.

MSC:
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K15 Initial value problems for second-order parabolic equations
80A20 Heat and mass transfer, heat flow (MSC2010)
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