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Finite element solutions of the non‐self‐adjoint convective‐dispersion equation
Author(s) -
Prakash Anand
Publication year - 1977
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620110205
Subject(s) - galerkin method , finite element method , mathematics , convergence (economics) , dispersion (optics) , stability (learning theory) , convection , mathematical analysis , variational principle , mechanics , physics , computer science , machine learning , optics , economics , thermodynamics , economic growth
Finite element formulations based on the Galerkin and variational principles have been developed for the self‐adjoint and non‐self‐adjoint problems represented respectively by the flow and convective‐dispersion equations in the cylindrical polar system of co‐ordinates. The formulation based on the variational principle is shown to be restricted to dispersion‐dominant transports only. The Galerkin method is demonstrated to be more versatile and free from convergence and stability problems. The computational scheme based on the Galerkin principle is shown to be equally valid for both convection and dispersion dominant transports. The numerical results obtained are verified with known analytical solutions. It is concluded that the suggested scheme can be used in solving a variety of field problems involving groundwater dispersion.