Browsing by Author "McGee, Wayne Michael"
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Item h-p-k least squares finite element methodology and implementation for fluid-structure interactions(Texas Tech University, 2007-12) McGee, Wayne Michael; Seshaiyer, Padmanabhan; Allen, Edward J.; Ibragimov, Akif; Manservisi, Sandro; Aulisa, EugenioAs the complexity of fully coupled physical modeling applications grows, both in the simultaneous representation of multiple types of physics as well as in the physical geometries of problem domains, the utility of directly specifiable, generally applicable, unconditionally consistent variational methodologies incorporated with conforming and nonconforming adaptive finite element discretizations becomes increasingly apparent. The intent of this dissertation is to describe the mathematical theory for a general problem-solving methodology, apply this theory to a particular one-dimensional fluid-structure interaction problem involving a moving mesh under an Arbitrary Lagrangian-Eulerian framework, representative of a particular two-dimensional problem of the same type in arterial blood flow analysis, and develop a C++ finite element component library for rapid modeling application development. We will present the complete fluid-structure application and some numerical error results verifying convergence of the method under h and p refinements for varying k values, where k is the order of global continuity of the finite element approximations.Item Three-dimensional mortar finite element method for convection-diffusion equation with nonconforming meshes(Texas Tech University, 2003-08) McGee, Wayne MichaelIn the last decade, non-conforming domain decomposition methods such as the mortar finite element method have been shown to be reliable techniques for several engineering applications that often employ complex finite element design. With this technique, one can conveniently assemble local subcomponents into a global domain without matching the finite element nodes of each subcomponent at the common interface. We employ the mortar finite element formulation in conjunction with higher-order elements, where both mesh refinement and degree enhancement are combined to increase accuracy. The mortar finite element method has proven to be a good candidate for implementation in two dimensions. In this work, for the first time, we present computational results for the convergence of the mortar finite element technique in three dimensions for the convection-diffusion equation. Our numerical results demonstrate optimality for the resulting non-conforming method for various mesh and polynomial degree discretizations.