Thesis (Ph. D.)--University of Missouri-Columbia, 2001. / Typescript. Vita. Includes bibliographical references (leaves 136-143). Also available on the Internet.

Thesis (Ph. D.)--Hong Kong University of Science and Technology, 2002. / Includes bibliographical references (leaves 145-150). Also available in electronic version. Access restricted to campus users.

Thesis (Ph.D.)--Brown University, 2008. / Vita. Advisor : Anubhav Tripathi. Includes bibliographical references.

Thesis (M. Sc.)--University of Alberta, 2009. / Title from pdf file main screen (viewed on Dec. 10, 2009). "A thesis submitted to the Faculty of Graduate Studies and Research in partial fulfillment of the requirements for the degree of Master of Science in Chemical Engineering, [Department of] Chemical and Materials Engineering, University of Alberta." Includes bibliographical references.

Thesis (Ph. D.)--Institute of Paper Chemistry, 1962. / Includes bibliographical references (p. 90-91).

Title from title page of PDF (University of Missouri--St. Louis, viewed February 23, 2010). Includes bibliographical references.

Thesis (Ph. D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, and the Woods Hole Oceanographic Institution), 2003. / Includes bibliographical references (p. 145-148).

This research deals with several novel aspects of finite element formulations and methodology in parallel adaptive simulation of flow problems. Composite macroelement schemes are developed for problems of thin fluid layers with deforming free surfaces or decomposing material phases; experiments are also run on divergence-free formulations that can be derived from the same element classes. The constrained composite nature and C¹ continuity requirements of these elements raises new issues, especially with respect to adaptive refinement patterns and the treatment of hanging node constraints, which are more complex than encountered with standard element types. This work combines such complex elements with these applications and with parallel adaptive mesh refinement and coarsening (AMR/C) techniques for the first time. The use of adaptive macroelement spaces also requires appropriate programming interfaces and data structures to enable easy and efficient implementation in parallel software. The algorithms developed for this work are implemented using object-oriented designs described herein. One application class of interest concerns heated viscous thin fluid layers that have a deformable free surface. These problems occur in both normal scale laboratory and industrial applications and in micro-fluidics. Modeling this flow via depth averaging gives a nonlinear boundary value problem describing the transient evolution of the film thickness. The model is dominated by surface tension effects which are described by a combination of nonlinear second and fourth-order operators. This research work also includes studies using the divergence-free forms constructed from these elements for certain classes of non-Newtonian fluids such as the Powell-Eyring and Williamson shear-thinning viscosity models. In addition to the target problems we conduct verification studies in support of the simulation development. In the final application investigated, C¹ elements are used in conforming finite element approximations of the Cahn-Hilliard phase field model for moving interface and phase separation problems. The nonlinear Cahn-Hilliard equation combines anti-diffusive configurational free energy based terms with a fourth-order interfacial free energy based term. Numerical studies include both manufactured and physically significant problems, including parametric studies of directed pattern self-assembly in phase decomposition of thin films. The main new contributions include construction of C¹ and div-free macroelement classes suitable for AMR/C with nonconforming hanging node meshes; a posteriori error estimation for fourth-order problems using these and other element classes; use of projection operators to automate the correct treatment of constraints at hanging nodes and through AMR/C steps; design of supporting data structures and algorithms for implementation in a parallel object oriented framework; variational formulations, methodology and numerical experiments with nonlinear fourth-order flow and transport models; and parametric and Monte Carlo studies of directed phase decomposition. / text

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