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The Resource A finite element primer for beginners : the basics, Tarek I. Zohdi

A finite element primer for beginners : the basics, Tarek I. Zohdi

Creator
Author
Summary
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations, (2) A model problem for one-dimensional?linear elastostatics, (3) Weak formulations in one dimension, (4) Minimum principles in one dimension, (5) Error estimation in one dimension, (5) Construction of Finite Element basis functions in one dimension, (6) Gaussian Quadrature, (7) Iterative solvers and element by element data structures, (8) A model problem for th
Language
eng
Work
Publication
Extent
1 online resource (ix, 108 pages)
Contents
  • Preface; Contents; 1 Weighted Residuals and Galerkin''s Method for a Generic 1-D Problem; 1.1 Introduction: Weighted Residual Methods ; 1.2 Galerkin''s Method; 1.3 An Overall Framework ; 2 A Model Problem: 1-D Elastostatics; 2.1 Introduction: A Model Problem; 2.2 Weak Formulations in One Dimension; 2.3 An Example; 2.4 Some Restrictions; 2.5 Remarks on Nonlinear Problems; References; 3 A Finite Element Implementation in One Dimension; 3.1 Introduction; 3.2 Finite Element Method Implementation; 3.3 FEM Approximation; 3.4 Construction of FEM Basis Functions
  • 3.5 Integration and Gaussian Quadrature3.5.1 An Example; 3.6 Global/Local Transformations; 3.7 Differential Properties of Shape Functions; 3.8 Postprocessing; 3.9 A Detailed Example; 3.9.1 Weak Form; 3.9.2 Formation of the Discrete System; 3.9.3 Applying Boundary Conditions; 3.9.4 Massive Data Storage Reduction; 3.10 Quadratic Elements; Reference; 4 Accuracy of the Finite Element Method; 4.1 Introduction ; 4.2 The ``Best Approximation'''' Theorem ; 4.3 An Error Bound; 4.4 The Principle of Minimum Potential Energy ; 4.5 Simple Estimates for Adequate FEM Meshes ; 4.6 Local Mesh Refinement
  • 7.6 Three-Dimensional Shape Functions7.7 Differential Properties of Shape Functions; 7.8 Differentiation in the Referential Coordinates; 7.8.1 Implementation Issues; 7.8.2 An Example of the Storage Scaling; 7.9 Surface Jacobians and Nanson''s Formula; 7.10 Postprocessing; References; 8 Accuracy of the Finite Element Method; 8.1 Introduction; 8.2 The ``Best Approximation'''' Theorem; 8.3 A Bound on the Error; 8.4 Simple Estimates for Adequate FEM Meshes -- Revisited for Three Dimensions; 8.5 Local Error Estimation and Adaptive Mesh Refinement; 8.5.1 A Posteriori Recovery Methods
  • 8.5.2 A Posteriori Residual MethodsReferences; 9 Time-Dependent Problems; 9.1 Introduction; 9.2 Generic Time Stepping; 9.3 Application to the Continuum Formulation; References; 10 Summary and Advanced Topics; References; Appendix AElementary Mathematical Concepts; Appendix BBasic Continuum Mechanics; Appendix Convergence of Recursive Iterative Schemes
Isbn
9783319090368
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-09036-8
Instance
Label
A finite element primer for beginners : the basics
Title
A finite element primer for beginners
Title remainder
the basics
Statement of responsibility
Tarek I. Zohdi
Creator
Author
Subject
Genre
Language
eng
Summary
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations, (2) A model problem for one-dimensional?linear elastostatics, (3) Weak formulations in one dimension, (4) Minimum principles in one dimension, (5) Error estimation in one dimension, (5) Construction of Finite Element basis functions in one dimension, (6) Gaussian Quadrature, (7) Iterative solvers and element by element data structures, (8) A model problem for th
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorName
Zohdi, Tarek I
Dewey number
518/.25
Illustrations
illustrations
Index
no index present
LC call number
TA347.F5
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
SpringerBriefs in Applied Sciences and Technology,
http://library.link/vocab/subjectName
  • Finite element method
  • MATHEMATICS
  • Finite element method
  • Engineering
  • Continuum Mechanics and Mechanics of Materials
  • Engineering Fluid Dynamics
  • Complexity
  • Computational Science and Engineering
  • Mathematical Modeling and Industrial Mathematics
  • Numerical and Computational Physics
Label
A finite element primer for beginners : the basics, Tarek I. Zohdi
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-09036-8
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1 Weighted Residuals and Galerkin''s Method for a Generic 1-D Problem; 1.1 Introduction: Weighted Residual Methods ; 1.2 Galerkin''s Method; 1.3 An Overall Framework ; 2 A Model Problem: 1-D Elastostatics; 2.1 Introduction: A Model Problem; 2.2 Weak Formulations in One Dimension; 2.3 An Example; 2.4 Some Restrictions; 2.5 Remarks on Nonlinear Problems; References; 3 A Finite Element Implementation in One Dimension; 3.1 Introduction; 3.2 Finite Element Method Implementation; 3.3 FEM Approximation; 3.4 Construction of FEM Basis Functions
  • 3.5 Integration and Gaussian Quadrature3.5.1 An Example; 3.6 Global/Local Transformations; 3.7 Differential Properties of Shape Functions; 3.8 Postprocessing; 3.9 A Detailed Example; 3.9.1 Weak Form; 3.9.2 Formation of the Discrete System; 3.9.3 Applying Boundary Conditions; 3.9.4 Massive Data Storage Reduction; 3.10 Quadratic Elements; Reference; 4 Accuracy of the Finite Element Method; 4.1 Introduction ; 4.2 The ``Best Approximation'''' Theorem ; 4.3 An Error Bound; 4.4 The Principle of Minimum Potential Energy ; 4.5 Simple Estimates for Adequate FEM Meshes ; 4.6 Local Mesh Refinement
  • 7.6 Three-Dimensional Shape Functions7.7 Differential Properties of Shape Functions; 7.8 Differentiation in the Referential Coordinates; 7.8.1 Implementation Issues; 7.8.2 An Example of the Storage Scaling; 7.9 Surface Jacobians and Nanson''s Formula; 7.10 Postprocessing; References; 8 Accuracy of the Finite Element Method; 8.1 Introduction; 8.2 The ``Best Approximation'''' Theorem; 8.3 A Bound on the Error; 8.4 Simple Estimates for Adequate FEM Meshes -- Revisited for Three Dimensions; 8.5 Local Error Estimation and Adaptive Mesh Refinement; 8.5.1 A Posteriori Recovery Methods
  • 8.5.2 A Posteriori Residual MethodsReferences; 9 Time-Dependent Problems; 9.1 Introduction; 9.2 Generic Time Stepping; 9.3 Application to the Continuum Formulation; References; 10 Summary and Advanced Topics; References; Appendix AElementary Mathematical Concepts; Appendix BBasic Continuum Mechanics; Appendix Convergence of Recursive Iterative Schemes
Dimensions
unknown
Extent
1 online resource (ix, 108 pages)
File format
unknown
Form of item
online
Isbn
9783319090368
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-09036-8
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)889033680
  • (OCoLC)ocn889033680
Label
A finite element primer for beginners : the basics, Tarek I. Zohdi
Link
https://ezproxy.lib.ou.edu/login?url=http://link.springer.com/10.1007/978-3-319-09036-8
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Preface; Contents; 1 Weighted Residuals and Galerkin''s Method for a Generic 1-D Problem; 1.1 Introduction: Weighted Residual Methods ; 1.2 Galerkin''s Method; 1.3 An Overall Framework ; 2 A Model Problem: 1-D Elastostatics; 2.1 Introduction: A Model Problem; 2.2 Weak Formulations in One Dimension; 2.3 An Example; 2.4 Some Restrictions; 2.5 Remarks on Nonlinear Problems; References; 3 A Finite Element Implementation in One Dimension; 3.1 Introduction; 3.2 Finite Element Method Implementation; 3.3 FEM Approximation; 3.4 Construction of FEM Basis Functions
  • 3.5 Integration and Gaussian Quadrature3.5.1 An Example; 3.6 Global/Local Transformations; 3.7 Differential Properties of Shape Functions; 3.8 Postprocessing; 3.9 A Detailed Example; 3.9.1 Weak Form; 3.9.2 Formation of the Discrete System; 3.9.3 Applying Boundary Conditions; 3.9.4 Massive Data Storage Reduction; 3.10 Quadratic Elements; Reference; 4 Accuracy of the Finite Element Method; 4.1 Introduction ; 4.2 The ``Best Approximation'''' Theorem ; 4.3 An Error Bound; 4.4 The Principle of Minimum Potential Energy ; 4.5 Simple Estimates for Adequate FEM Meshes ; 4.6 Local Mesh Refinement
  • 7.6 Three-Dimensional Shape Functions7.7 Differential Properties of Shape Functions; 7.8 Differentiation in the Referential Coordinates; 7.8.1 Implementation Issues; 7.8.2 An Example of the Storage Scaling; 7.9 Surface Jacobians and Nanson''s Formula; 7.10 Postprocessing; References; 8 Accuracy of the Finite Element Method; 8.1 Introduction; 8.2 The ``Best Approximation'''' Theorem; 8.3 A Bound on the Error; 8.4 Simple Estimates for Adequate FEM Meshes -- Revisited for Three Dimensions; 8.5 Local Error Estimation and Adaptive Mesh Refinement; 8.5.1 A Posteriori Recovery Methods
  • 8.5.2 A Posteriori Residual MethodsReferences; 9 Time-Dependent Problems; 9.1 Introduction; 9.2 Generic Time Stepping; 9.3 Application to the Continuum Formulation; References; 10 Summary and Advanced Topics; References; Appendix AElementary Mathematical Concepts; Appendix BBasic Continuum Mechanics; Appendix Convergence of Recursive Iterative Schemes
Dimensions
unknown
Extent
1 online resource (ix, 108 pages)
File format
unknown
Form of item
online
Isbn
9783319090368
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Note
SpringerLink
Other control number
10.1007/978-3-319-09036-8
Other physical details
illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • (OCoLC)889033680
  • (OCoLC)ocn889033680

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