The Use of Galerkin Finite-Element Methods to Solve Mass-Transport Equations
D. Grove. Water-Resources Investigations, USGS/WRI-77-49. U. S. Geological Survey, Denver, (October 1977)
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
found to be 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.
%0 Report
%1 grove1977galerkin
%A Grove, David B.
%C Denver
%D 1977
%K 35k57-reaction-diffusion-equations 76m10-finite-element-methods-in-fluid-mechanics 76s05-flows-in-porous-media 80a20-heat-and-mass-transfer U method-of-characteristics
%N USGS/WRI-77-49
%T The Use of Galerkin Finite-Element Methods to Solve Mass-Transport Equations
%U https://pubs.usgs.gov/wri/1977/0049/report.pdf
%X 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
found to be 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.
@techreport{grove1977galerkin,
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
found to be 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.},
added-at = {2021-07-26T08:42:57.000+0200},
address = {Denver},
author = {Grove, David B.},
biburl = {https://www.bibsonomy.org/bibtex/23594ecf16b80bd45a9406b7495921c67/gdmcbain},
institution = {U. S. Geological Survey},
interhash = {579f1d6dfa4414ea003c028e79eb4c81},
intrahash = {3594ecf16b80bd45a9406b7495921c67},
keywords = {35k57-reaction-diffusion-equations 76m10-finite-element-methods-in-fluid-mechanics 76s05-flows-in-porous-media 80a20-heat-and-mass-transfer U method-of-characteristics},
month = oct,
number = {USGS/WRI-77-49},
timestamp = {2021-07-26T08:44:02.000+0200},
title = {The Use of {G}alerkin Finite-Element Methods to Solve Mass-Transport Equations},
type = {Water-Resources Investigations},
url = {https://pubs.usgs.gov/wri/1977/0049/report.pdf},
year = 1977
}