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Table of Contents:

Chapter 1: Introduction
1.1 Background of the Study
1.2 Research Aim and Objectives
1.3 Significance of the Study
1.4 Research Questions
1.5 Structure of the Thesis

Chapter 2: Literature Review
2.1 Overview of Navier-Stokes Equations
2.2 Finite Element Method
2.3 Previous Studies on Approximating Navier-Stokes Equations
2.4 Gaps in Existing Literature

Chapter 3: Research Methodology
3.1 Research Design
3.2 Data Collection Methods
3.3 Data Analysis Techniques
3.4 Validation of Results

Chapter 4: Discussion of Findings
4.1 Analysis of Results
4.2 Comparison with Existing Methods
4.3 Implications of Findings
4.4 Recommendations for Future Research

Chapter 5: Conclusion and Summary
5.1 Summary of Findings
5.2 Contributions to the Field
5.3 Limitations of the Study
5.4 Conclusion and Future Directions

Brief Overview:

The thesis “Approximating Navier-Stokes equations using finite elements” aims to explore the application of finite element method in approximating the Navier-Stokes equations, which are fundamental equations in fluid dynamics. The study will provide an in-depth analysis of the existing literature on the topic, identify gaps in current research, and propose a novel approach to solving the equations.

Chapter 1 introduces the background, aim, objectives, and significance of the study, as well as the research questions to be addressed. Chapter 2 presents a comprehensive review of the Navier-Stokes equations and finite element method, along with a discussion of previous studies in the field. Chapter 3 outlines the research methodology, including the design, data collection methods, analysis techniques, and validation of results.

In Chapter 4, the findings of the study are discussed, including an analysis of the results, comparison with existing methods, implications of the findings, and recommendations for future research. Finally, Chapter 5 provides a summary of the findings, contributions to the field, limitations of the study, and concludes with suggestions for future directions in research on approximating Navier-Stokes equations using finite elements.

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