Approximation of Elliptic Boundary-Value Problems (Dover Books on Mathematics)
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Book Details
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Author: Jean-Pierre Aubin
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Publisher: Dover
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Binding: Paperback
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Number of Pages: 356
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Release Date: 27-02-2007
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ISBN: 9780486457918
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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.