Authors

Lu ZhangFollow

Abstract

Discontinuous Galerkin methods are widely used in many practical fields. In this thesis, we focus on a new class of discontinuous Galerkin methods for second-order wave equations. This thesis is constructed by three main parts. In the first part, we study the convergence properties of the energy-based discontinuous Galerkin proposed in [3] for wave equations. We improve the existing suboptimal error estimates to an optimal convergence rate in the energy norm. In the second part, we generalize the energy-based discontinuous Galerkin method proposed in [3] to the advective wave equation and semilinear wave equation in second-order form. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the interelement fluxes. Error estimates in the energy norm are established. In the third part, we focus on establishing methods to overcome the computa- tional stiffness from the high-order piecewise polynomial approximations in the energy-based discontinuous Galerkin methods and reduce the computational cost of the inversion of the stiffness matrix.

Degree Date

2020

Document Type

Dissertation

Degree Name

Ph.D.

Department

Mathematics

Advisor

Thomas Hagstrom

Subject Area

Mathematics, Applied

Number of Pages

158

Format

.pdf

Creative Commons License

Creative Commons Attribution-Noncommercial 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial 4.0 License

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