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Approximation of Elliptic Boundary-Value Problems (Dover Books on Mathematics)

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Book Details

  • Author: Jean-Pierre Aubin

  • Publisher: Dover

  • Binding: Paperback

  • Number of Pages: 356

  • Release Date: 27-02-2007

  • ISBN: 9780486457918

  • Language: English

About The Book

The Finite-Element Method for Boundary-Value Problems presents a detailed exploration of the finite-element method (FEM), specifically combining it with variational methods for solving boundary-value problems. Unlike the finite-difference method, FEM is a more advanced and effective approach, particularly for nonhomogeneous boundary-value problems involving elliptic operators. This self-contained text is ideal for advanced undergraduates and graduate students, offering both a theoretical foundation and practical insights into the applications of FEM.

The book begins with a comprehensive introduction to variational and finite-difference methods for second-order differential equations. From there, it progresses to more abstract concepts, such as approximations of Hilbert spaces and linear operators, before diving into the heart of finite-element approximations of Sobolev spaces. Later chapters focus on the approximation of nonhomogeneous boundary-value problems, providing a deeper understanding of the practical and theoretical underpinnings of FEM.

Through its well-structured chapters and thorough explanations, the book ensures that readers gain a solid understanding of both the mathematical theory and the real-world applications of FEM, making it an essential resource for those pursuing advanced studies in applied mathematics, physics, and engineering.