Please use this identifier to cite or link to this item: http://hdl.handle.net/10603/14695
Title: Mixed Galerkin finite element methods for fourth order differential equations
Researcher: Nandini A P
Guide(s): Jones Tarcius Doss, L.
Keywords: Petrov-Galerkin, Fisher-Kolmogorov equation, Galerkin mixed finite element method
Upload Date: 6-Jan-2014
University: Anna University
Completed Date: 
Abstract: The work presented in this thesis is on numerical schemes, optimal order a priori error estimates and computational experiments for fourth order differential equations using mixed Galerkin finite element methods. Two types of ordinary differential equations and two types of nonlinear time-dependent partial differential equations of fourth order in single space variable are considered. A quadrature based mixed Petrov-Galerkin finite element method is applied to a special type of fourth order linear ordinary differential equation in divergence form. The integrals are then replaced by Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh. The same method is then applied to a general fourth order linear ordinary differential equation and optimal order a priori error estimates are obtained without any restriction on the mesh. These error estimates are validated by a numerical example. An H1-Galerkin mixed finite element method is applied to the extended Fisher-Kolmogorov equation, a nonlinear time dependent fourth order partial differential equation, employing a splitting technique. This method may also be considered as a Petrov-Galerkin method with cubic spline space as trial space and piecewise linear space as test space, since second derivative of a cubic spline is a linear spline. A fully discrete scheme is also developed and optimal order a priori error estimates are obtained. The results are validated with numerical examples. A similar method is applied to the Kuramoto-Sivashinsky equation which is also a nonlinear time dependent fourth order partial differential equation. By employing a splitting technique, optimal order a priori error estimates are obtained without any restriction on the mesh. A fully discrete scheme is also discussed and optimal order a priori error estimates are obtained. The results are validated with numerical examples. newline newline newline
Pagination: xv, 136
URI: http://hdl.handle.net/10603/14695
Appears in Departments:Faculty of Science and Humanities

Files in This Item:
File Description SizeFormat 
01_title.pdfAttached File28.74 kBAdobe PDFView/Open
02_certificates.pdf1.37 MBAdobe PDFView/Open
03_abstract.pdf17.64 kBAdobe PDFView/Open
04_acknowledgement.pdf296.1 kBAdobe PDFView/Open
05_contents.pdf41.48 kBAdobe PDFView/Open
06_chapter 1.pdf110.93 kBAdobe PDFView/Open
07_chapter 2.pdf139.42 kBAdobe PDFView/Open
08_chapter 3.pdf153.06 kBAdobe PDFView/Open
09_chapter 4.pdf268.03 kBAdobe PDFView/Open
10_chapter 5.pdf627.94 kBAdobe PDFView/Open
11_chapter 6.pdf44.85 kBAdobe PDFView/Open
12_references.pdf46.04 kBAdobe PDFView/Open
13_publications.pdf17.88 kBAdobe PDFView/Open
14_vitae.pdf12.56 kBAdobe PDFView/Open


Items in Shodhganga are protected by copyright, with all rights reserved, unless otherwise indicated.