Some numerical and theoretical results on a two-dimensional dam overflow problem

Abstract

The thesis consists of four chapters and two appendixes. In the first chapter, background of the Dam Overflow problem, the Sobolev spaces, the Finite Element Method as well as other basic PDE concepts are introduced. This chapter also includes and extensive review of the existing related materials. In Chapter 2, the proposed algorithm of the potential function model is presented. Furthermore, a relaxation factor method is adopted in the thesis to achieve a better algorithm for running faster and more stably. In Chapter 3, some theoretical results as well as numerical results are obtained for the stream function model. In Chapter 4, the two methods using the potential function model and the stream function model are compared. Chapter 2, Chapter 3 and Chapter 4 are my major work on the field of the Dam Overflow Problem. In Chapter 5 some reviews on my work are given and some possible directions for future research are indicated. In Appendix A, all the theorems used in this thesis are listed, and in Appendix B, a powerful software called "Finite Element Program Generator (FEPG)" is briefly introduced. The FEPG provides a powerful and convenient tool for coding my programs for the present work.