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A comprehensive reference on the theory and practice of computational mechanics. This book aims to serve as the foundation for research and practice in developing designs and in understanding, assessing, and managing numerical analysis systems.
Sommario
VOLUME 1: FUNDAMENTALS.
List of Contributors.
Preface.
1. Fundamentals, Introduction and Survey ( ErwinStein).
Motivation and Scope.
2. Finite Difference Methods ( Owe Axelsson).
Introduction.
Two-point Boundary Value Problems.
Finite Difference Methods for Elliptic Problems.
Finite Difference Methods for Parabolic Problems.
Finite Difference Methods for Hyperbolic Problems.
Convection--Diffusion Problems.
A Summary of Difference Schemes.
References.
Further Reading.
3. Interpolation in h -version Finite Element Spaces( Thomas Apel)..
Introduction.
Finite Elements.
Definition of Interpolation Operators.
The Deny--Lions Lemma.
Local Error Estimates for the Nodal Interpolant.
Local Error Estimates for Quasi-Interpolants.
Example for a Global Interpolation Error Estimate.
Related Chapters.
References.
4. Finite Element Methods ( Susanne C. Brenner and CarstenCarstensen).
Introduction.
Ritz--Galerkin Methods for Linear Elliptic Boundary ValueProblems.
Finite Element Spaces.
A Priori Error Estimates for Finite Element Methods.
A Posteriori Error Estimates and Analysis.
Local Mesh Refinement.
Other Aspects.
Acknowledgments.
References.
Further Reading.
5. The p -version of the Finite Element Method( Ernst Rank, Barna Szabó; and AlexanderDüster).
Introduction.
Implementation.
Convergence Characteristics.
Performance Characteristics.
Applications to Nonlinear Problems.
Outlook.
Acknowledgements.
Notes.
References.
Further Reading.
6. Spectral Methods ( Claudio Canuto and AlfioQuarteroni).
Introduction.
Fourier Methods.
Algebraic Polynomial Expansion.
Algebraic Expansions on Triangles.
Stokes and Navier--Stokes Equations.
Advection Equations and Conservation Laws.
The Spectral Element Method.
The Mortar Method.
References.
7. Adaptive Wavelet Techniques in Numerical Simulation( Wolfgang Dahmen, Ronald DeVore and Albert Cohen).
Introduction.
Wavelets.
Evolution Problems---Compression of Flow Fields.
Boundary Integral Equations---Matrix Compression.
A New Adaptive Paradigm.
Construction of Residual Approximations and ComplexityAnalysis.
Acknowledgment.
Notes.
References.
Further Reading.
8. Plates and Shells: Asymptotic Expansions and HierarchicModels ( Zohar Yosibash, Monique Dauge and ErwanFaou).
Introduction.
Multiscale Expansions for Plates.
Hierarchical Models for Plates.
Multiscale Expansions and Limiting Models for Shells.
Hierarchical Models for Shells.
Finite Element Methods in thin Domains.
Acknowledgments.
References.
Further Reading.
9. Mixed Finite Elements Methods ( Franco Brezzi,Ferdinando Auricchio and Carlo Lovadina).
Introduction.
Formulations.
Stability of Saddle-Points in Finite Dimensions.
Applications.
Techniques for Proving the inf--sup Condition.
References.
10. Meshfree Methods ( Timon Rabczuk, Ted Belytschko, SoniaFernández-Méndez and Antonio Huerta).
Introduction.
Approximation in Meshfree Methods.
Discretization of Partial Differential Equations.
Radial Basis Functions.
Discontinuities.
Blending Meshfree Methods and Finite Elements.
References.
11. Discrete Element Method ( NenadBicanic).
Introduction.
Basic Discrete Element Framework and Regularization of NonsmoothContact Conditions.
Characterization of Interacting Bodies and ContactDetection.
Imposition of Contact Constraints and Boundary Conditions.
Modeling of Block Deformability.
Transition Continuum/Discontinuum, Fragmentation in DiscreteElement Methods.
Time Integration---Temporal Discretization, Energy Balance, andDiscrete Element Implementation.
Associated Frameworks and Developments.
References.
Further Reading.
12. Boundary Element Methods: Foundation and Error Analysis( W. L. Wendland and G. C. Hsiao).
Introduction.
Boundary Integral
Relazione
"This three volume set provides the most comprehensive andup-to-date collection of knowledge about this increasinglyimportant area of engineering science. The Encyclopedia provides awell-rounded and practical knowledge base that will serve as afoundation for the reader s research and practice in developingdesigns and in understanding, assessing and managing numericalanalysis systems." ( Zentralblatt MATH, 2010)
