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京都大学 / 新制・課程博士 / 博士(人間・環境学) / 甲第25366号 / 人博第1108号 / 京都大学大学院人間・環境学研究科共生人間学専攻 / (主査)教授 日置 尋久, 教授 立木 秀樹, 准教授 櫻川 貴司, 准教授 深沢 圭一郎, 教授 小山田 耕二 / 学位規則第4条第1項該当 / Doctor of Human and Environmental Studies / Kyoto University / DGAM

For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75. For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.

In this thesis we are concerned with the numerical simulation of the in- teraction of compressible viscous flow and an elastic structure in 2D. For the elastic deformation we use a 2D linear model and nonlinear St. Venant- Kirchhoff and neo-Hookean models. The flow is described by the compressible Navier-Stokes equations written in the arbitrary Lagrangian-Eulerian (ALE) form in order to take into account the time-dependence of the flow domain. The discretization of both the flow problem and the elasticity problem is re- alized by the discontinuous Galerkin finite element method (DGM). We focus on testing the DGM applied to the solution of the flow and elasticity prob- lems. Furthermore, we discuss the coupling algorithm and the technique, how to deal with the deformation of the computational domain for the fluid flow problem. Our work is motivated by the biomedical applications. Numerical experiments include numerical simulation of vibrations of human vocal folds induced by the compressible viscous flow.

For a class of two-dimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened Cauchy-Buniakowski-Schwarz (C.B.S.) inequality in the cases of h -hierarchical and p -hierarchical finite element discretizations with triangular meshes differ by the factor 0.75. For plane linear elasticity problems and triangulations with right isosceles tri- angles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for three-dimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.