Publication Date

Summer 7-17-2017

Abstract

Many real-world problems involving dynamics of solid or fluid bodies can be modeled by hyperbolic partial differential equations (PDEs). Up to this point, only solutions to selected PDEs are available. Many PDEs are physically or geometrically complex, resulting in difficulties computing the analytical solutions. In this thesis, we focus on numerical methods for approximating solutions to hyperbolic PDEs. Long-term simulation for the motion of the body described by the PDE requires a method that is not only robust and efficient, but also produces small error because the error will be propagated and accumulated over the course of the simulation. Therefore, we use the so-called high order methods. In particular, we study Hermite methods and Sobolev Discontinuous Galerkin methods. This thesis describes my contribution to two high order methods, which includes the development of flux-conservative Hermite methods for nonlinear PDEs of conservation law type and Sobolev Discontinuous Galerkin methods for general hyperbolic PDEs.

Degree Name

Mathematics

Level of Degree

Doctoral

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Daniel Appel\"{o}

Second Committee Member

Stephen Lau

Third Committee Member

Jens Lorenz

Fourth Committee Member

Thomas Hagstrom

Language

English

Document Type

Dissertation

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