Type of Document	Master's Thesis
Author	Smith, Lyle C. III
Author's Email Address	lylesmith3@yahoo.com
URN	etd-7697-194740
Title	Finite Element Approximations of Burgers' Equation with Robin's Boundary Conditions
Degree	Master of Science
Department	Mathematics
Advisory Committee	Advisor Name Title Herdman, Terry L. Rogers, Robert C. Burns, John A. Committee Chair
Keywords	Finite Elements
Date of Defense	1997-07-31
Availability	unrestricted
Abstract This work is a numerical study of Burgers’ equation with Robin’s boundary conditions. The goal is to determine the behavior of the solutions in the limiting cases of Dirichlet and Neumann boundary conditions. We develop and test two separate finite element and Galerkin schemes. The Galerkin/Conservation method is shown to give better results and is then used to compute the response as the Robin’s Boundary conditions approach both the Dirichlet and Neumann boundary conditions. Burgers’ equation is treated as a perturbation of the linear heat equation with the appropriate realistic constants. The goal is to determine if the use of the Robin’s boundary conditions to approximate Dirichlet and Neumann boundary conditions affords any advantage over schemes that employ only “exact” Dirichlet or Neumann boundary conditions. Our finite element results indicate that solutions using appropriate Robin’s boundary conditions approach the same solutions obtained by “exact” Dirichlet or Neumann boundary conditions. This allows us to obtain realistic solutions in some cases where the other schemes had previously failed.
Files	Filename       Size       Approximate Download Time (Hours:Minutes:Seconds)     28.8 Modem   56K Modem   ISDN (64 Kb)   ISDN (128 Kb)   Higher-speed Access    FIG321.PDF 28.87 Kb 00:00:08 00:00:04 00:00:03 00:00:01 < 00:00:01   FIG3210.PDF 138.80 Kb 00:00:38 00:00:19 00:00:17 00:00:08 < 00:00:01   FIG3211.PDF 89.35 Kb 00:00:24 00:00:12 00:00:11 00:00:05 < 00:00:01   FIG3212.PDF 148.55 Kb 00:00:41 00:00:21 00:00:18 00:00:09 < 00:00:01   FIG3213.PDF 260.16 Kb 00:01:12 00:00:37 00:00:32 00:00:16 00:00:01   FIG3214.PDF 468.14 Kb 00:02:10 00:01:06 00:00:58 00:00:29 00:00:02   FIG3215.PDF 89.73 Kb 00:00:24 00:00:12 00:00:11 00:00:05 < 00:00:01   FIG3216.PDF 149.60 Kb 00:00:41 00:00:21 00:00:18 00:00:09 < 00:00:01   FIG3217.PDF 261.27 Kb 00:01:12 00:00:37 00:00:32 00:00:16 00:00:01   FIG3218.PDF 469.54 Kb 00:02:10 00:01:07 00:00:58 00:00:29 00:00:02   FIG322.PDF 21.34 Kb 00:00:05 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG323.PDF 32.44 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01   FIG324.PDF 52.50 Kb 00:00:14 00:00:07 00:00:06 00:00:03 < 00:00:01   FIG325.PDF 99.32 Kb 00:00:27 00:00:14 00:00:12 00:00:06 < 00:00:01   FIG326.PDF 21.38 Kb 00:00:05 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG327.PDF 32.44 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01   FIG328.PDF 52.52 Kb 00:00:14 00:00:07 00:00:06 00:00:03 < 00:00:01   FIG329.PDF 98.44 Kb 00:00:27 00:00:14 00:00:12 00:00:06 < 00:00:01   FIG331.PDF 746.53 Kb 00:03:27 00:01:46 00:01:33 00:00:46 00:00:03   FIG332.PDF 95.01 Kb 00:00:26 00:00:13 00:00:11 00:00:05 < 00:00:01   FIG333.PDF 96.37 Kb 00:00:26 00:00:13 00:00:12 00:00:06 < 00:00:01   FIG334.PDF 100.04 Kb 00:00:27 00:00:14 00:00:12 00:00:06 < 00:00:01   FIG335.PDF 71.87 Kb 00:00:19 00:00:10 00:00:08 00:00:04 < 00:00:01   FIG336.PDF 136.07 Kb 00:00:37 00:00:19 00:00:17 00:00:08 < 00:00:01   FIG341.PDF 23.48 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG342.PDF 14.48 Kb 00:00:04 00:00:02 00:00:01 < 00:00:01 < 00:00:01   FIG343.PDF 20.35 Kb 00:00:05 00:00:02 00:00:02 00:00:01 < 00:00:01   FIG344.PDF 22.08 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG345.PDF 32.92 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01   FIG346.PDF 31.75 Kb 00:00:08 00:00:04 00:00:03 00:00:01 < 00:00:01   FIG347.PDF 21.92 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG348.PDF 34.67 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01   FIG349.PDF 34.55 Kb 00:00:09 00:00:04 00:00:04 00:00:02 < 00:00:01   FIG351.PDF 24.39 Kb 00:00:06 00:00:03 00:00:03 00:00:01 < 00:00:01   FIG3510.PDF 273.37 Kb 00:01:15 00:00:39 00:00:34 00:00:17 00:00:01   FIG352.PDF 23.93 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG353.PDF 24.24 Kb 00:00:06 00:00:03 00:00:03 00:00:01 < 00:00:01   FIG354.PDF 24.00 Kb 00:00:06 00:00:03 00:00:03 00:00:01 < 00:00:01   FIG355.PDF 24.75 Kb 00:00:06 00:00:03 00:00:03 00:00:01 < 00:00:01   FIG356.PDF 23.50 Kb 00:00:06 00:00:03 00:00:02 00:00:01 < 00:00:01   FIG357.PDF 269.19 Kb 00:01:14 00:00:38 00:00:33 00:00:16 00:00:01   FIG358.PDF 259.35 Kb 00:01:12 00:00:37 00:00:32 00:00:16 00:00:01   FIG359.PDF 273.10 Kb 00:01:15 00:00:39 00:00:34 00:00:17 00:00:01   THESIS.PDF 442.72 Kb 00:02:02 00:01:03 00:00:55 00:00:27 00:00:02   VITA.PDF 3.61 Kb 00:00:01 < 00:00:01 < 00:00:01 < 00:00:01 < 00:00:01

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