%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 }