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The finite element method is a key tool in numerically solving partial differential equations. This book provides a fundamental and practical introduction to the method, its variants, and applications. Concepts are introduced in a straightforward manner while maintaining rigorous treatment without unnecessary abstraction. The content is based on a graduate course taught at Southern Methodist University and has also been used in seminar notes at Purdue University, the University of Minnesota, and Texas A&M University. Additionally, it served as the foundation for summer schools on the finite element method and its applications in various countries, including China, Iran, Mexico, and Venezuela. The book covers six major topics and four applications. Chapter 1 introduces the standard (H- and H²-conforming) finite element method. Chapters 2 and 3 discuss closely related methods: the nonconforming and mixed finite element methods. Chapters 4 and 5 focus on the recently developed discontinuous and characteristic finite element methods. Chapter 6 examines the adaptive finite element method. The final chapters apply these methods to solid mechanics (Chapter 7), fluid mechanics (Chapter 8), fluid flow in porous media (Chapter 9), and semiconductor modeling (Chapter 10).
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Finite element methods and their applications, Zhangxin Chen
- Lingua
- Pubblicato
- 2005
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- (Copertina rigida)
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