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The use of Galerkin finite-element methods to solve mass-transport equations

Water-Resources Investigations Report 77-49
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https://doi.org/10.3133/wri7749

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Abstract

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Suggested Citation

Grove, D.B., 1977, The use of Galerkin finite-element methods to solve mass-transport equations: U.S. Geological Survey Water-Resources Investigations Report 77-49, v, 55 p. :ill., maps ;27 cm., https://doi.org/10.3133/wri7749.

Publication type Report
Publication Subtype USGS Numbered Series
Title The use of Galerkin finite-element methods to solve mass-transport equations
Series title Water-Resources Investigations Report
Series number 77-49
DOI 10.3133/wri7749
Year Published 1977
Language ENGLISH
Publisher U.S. Dept. of the Interior, Geological Survey,
Description v, 55 p. :ill., maps ;27 cm.
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