h-p-k least squares finite element methodology and implementation for fluid-structure interactions
McGee, Wayne Michael
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As 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.