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Finite Element Methods [electronic resource] : A Practical Guide / by Jonathan Whiteley.

By: Whiteley, Jonathan [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Mathematical Engineering: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XI, 232 p. 28 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319499710.Subject(s): Mechanics, Applied | Solids | Differential equations | Numerical analysis | Mathematical models | Engineering mathematics | Engineering—Data processing | Solid Mechanics | Differential Equations | Numerical Analysis | Mathematical Modeling and Industrial Mathematics | Mathematical and Computational Engineering ApplicationsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620.105 Online resources: Click here to access online
Contents:
An overview of the finite element method -- A first example -- Linear boundary value problems -- Higher order basis functions -- Nonlinear boundary value problems -- Systems of ordinary differential equations -- Linear elliptic partial differential equations -- More general elliptic problems -- Quadrilateral elements -- Higher order basis functions -- Nonlinear elliptic partial differential equations -- Systems of elliptic equations -- Parabolic partial differential equations.
In: Springer Nature eBookSummary: This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
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An overview of the finite element method -- A first example -- Linear boundary value problems -- Higher order basis functions -- Nonlinear boundary value problems -- Systems of ordinary differential equations -- Linear elliptic partial differential equations -- More general elliptic problems -- Quadrilateral elements -- Higher order basis functions -- Nonlinear elliptic partial differential equations -- Systems of elliptic equations -- Parabolic partial differential equations.

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

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