Finite Element Approximation of Boundary Value Problems
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Beschreibung
This textbook provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience. The author accomplishes this, in part, by including numerous exercises and illustrations. Each chapter begins with a clear outline to help make complex concepts more approachable without sacrificing depth. Structurally, the book begins with the simplest type of finite element method: low order, piecewise continuous, Lagrange finite elements. With this, crucial questions about the stability and approximation errors are answered. Of particular note is the author’s coverage of two specific topics that often go overlooked in introductory material. The first is the numerical treatment of boundary conditions, especially the Nitsche technique. The second is a detailed explanation of the discretization error using specific techniques of a posteriori error estimation. With the book’s compact yet thorough treatment of these areas, readers will have a clear understanding of how mathematical analysis tools can be used in practice. Finite Element Approximation of Boundary Value Problems will be suitable as a supplementary textbook in applied mathematics courses for graduate students, and may also be used for self-study.
This textbook provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience. The author accomplishes this, in part, by including numerous exercises and illustrations. Each chapter begins with a clear outline to help make complex concepts more approachable without sacrificing depth. Structurally, the book begins with the simplest type of finite element method: low order, piecewise continuous, Lagrange finite elements. With this, crucial questions about the stability and approximation errors are answered. Of particular note is the author’s coverage of two specific topics that often go overlooked in introductory material. The first is the numerical treatment of boundary conditions, especially the Nitsche technique. The second is a detailed explanation of the discretization error using specific techniques of a posteriori error estimation. With the book’s compact yet thorough treatment of these areas, readers will have a clear understanding of how mathematical analysis tools can be used in practice. Finite Element Approximation of Boundary Value Problems will be suitable as a supplementary textbook in applied mathematics courses for graduate students, and may also be used for self-study.
Provides an accessible introduction to the mathematical foundations of the finite element method for a broad audience Presents numerous exercises, illustrations, and outlines to make complex topics more approachable Emphasizes the importance of two often overlooked topics: boundary conditions and the discretization error
Autor*in
Franz Chouly
Themen in »Finite Element Approximation of Boundary Value Problems«
Finite Element Method Nitsche finite element method Nitsche Signorini A posteriori error estimation Boundary value problems Lagrange finite elements Discretization error Dirichlet boundary condition Neumann boundary condition Lipschitz domains Sobolev spaces Poisson’s problem Deny-Lions theorem
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“This book gives a compact and concise introduction to finite element methods for elliptic boundary value problems. ... The book consists of seven chapters and an appendix. Each starts with an introductory outlook and ends with further comments. ... This book is well suited for self-study or a first-term-course at the advanced undergraduate or starting graduate level.” (Rüdiger Verfürth, Mathematical Reviews, July, 2026)
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