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Summary
Summary
Over the past four decades computational methods in applied mechanics have developed into valuable tools that are widely used across both industry and academia. The applications are numerous: aerospace structures, civil engineering structures, geotechnics, flow problems, automotive industry, geo-environmental modelling, biomechanics, electromagnetism, metal forming, to name but a few.
This three volume set provides the most comprehensive and up-to-date collection of knowledge about this increasingly important area of engineering science. The Encyclopedia provides a well-rounded and practical knowledge base that will serve as a foundation for the reader's research and practice in developing designs and in understanding, assessing and managing numerical analysis systems.
Containing over 70 in-depth and thoroughly cross referenced articles on key topics from internationally renowned researchers, the Encyclopedia of Computational Mechanics will cover three key areas.
Volume One: Fundamentals will cover the basic concepts behind discretization, interpolation, error estimation, solvers, computer algebra and geometric modelling. Volume Two: Solids and Volume Three: Fluids will build on this foundation with extensive, in-depth coverage of industrial applications.The main readership for this book will be researchers, research students (PhD. D. and postgraduate) and professional engineers in industrial and governmental laboratories. Academic interest will stem from civil, mechanical, geomechanical, biomedical, aerospace and chemical engineering departments, through to the fields of applied mathematics, computer science and physics.
Table of Contents
| Volume 1 Fundamentals |
| List of Contributors |
| Preface |
| 1 Fundamentals, Introduction and SurveyErwin Stein |
| Motivation and Scope |
| 2 Finite Difference MethodsOwe 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 inh-version Finite Element SpacesThomas 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 MethodsSusanne C. Brenner and Carsten Carstensen |
| Introduction |
| Ritz--Galerkin Methods for Linear Elliptic Boundary Value Problems |
| 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 Thep-version of the Finite Element MethodErnst Rank and Barna Szab?? and Alexander D8ster |
| Introduction |
| Implementation |
| Convergence Characteristics |
| Performance Characteristics |
| Applications to Nonlinear Problems |
| Outlook |
| Acknowledgements |
| Notes |
| References |
| Further Reading |
| 6 Spectral MethodsClaudio Canuto and Alfio Quarteroni |
| 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 SimulationWolfgang Dahmen and 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 Complexity Analysis |
| Acknowledgment |
| Notes |
| References |
| Further Reading |
| 8 Plates and Shells: Asymptotic Expansions and Hierarchic ModelsZohar Yosibash and Monique Dauge and Erwan Faou |
| 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 MethodsFranco Brezzi and 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 MethodsTimon Rabczuk and Ted Belytschko and Sonia Fern?-ndez-MA?ndez 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 MethodNenad BiA?aniA? |
| Introduction |
| Basic Discrete Element Framework and Regularization of Nonsmooth Contact Conditions |
| Characterization of Interacting Bodies and Contact Detection |
| Imposition of Contact Constraints and Boundary Conditions |
| Modeling of Block Deformability |
| Transition Continuum/Discontinuum, Fragmentation in Discrete Element Methods |
| Time |
