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Record Nr. |
UNINA9910983055803321 |
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Autore |
Chouly Franz |
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Titolo |
Finite Element Approximation of Boundary Value Problems / / by Franz Chouly |
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Pubbl/distr/stampa |
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Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025 |
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ISBN |
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9783031725302 |
9783031725296 |
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Edizione |
[1st ed. 2025.] |
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Descrizione fisica |
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1 online resource (161 pages) |
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Collana |
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Compact Textbooks in Mathematics, , 2296-455X |
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Disciplina |
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Soggetti |
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Numerical analysis |
Differential equations |
Numerical Analysis |
Differential Equations |
Anàlisi numèrica |
Equacions diferencials |
Llibres electrònics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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-- Introduction. -- A simple mathematical model. -- Low order Lagrange Finite Elements. -- The standard Finite Element Method. -- Nitsche Finite Element Method. -- Nitsche for Signorini. -- About meshing and discretization error. |
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Sommario/riassunto |
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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 |
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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. |
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