NOTES PERTAINING TO PUBLICATION, DISTRIBUTION, ETC.
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Electronic
INTERNAL BIBLIOGRAPHIES/INDEXES NOTE
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Includes bibliographical references (p. 323-344) and index. 0
CONTENTS NOTE
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"The objective [of this book] is to present the fundamentals of stabilized finite element methods for the analysis of steady and time-dependent convection-diffusion and fluid dynamics problems with an engineering rather than a mathematical bias." -- p.i.
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5. Unsteady convection-diffusion problems -- 5.1. Introduction -- 5.2. Problem statement -- 5.3. Time discretization procedures -- 5.4. Spatial discretization procedures -- 5.5. Stabilized space-time formulations -- 5.6. Solved exercises -- App. Least-squares in transient/relaxation problems -- 6. Viscous incompressible flows -- 6.1. Introduction -- 6.2. Basic concepts -- 6.3. Main issues in incompressible flow problems -- 6.4. Trial solutions and weighting functions -- 6.5. Stationary Stokes problem -- 6.6. Steady Navier-Stokes problem -- 6.7. Unsteady Navier-Stokes equations -- 6.8. Applications and solved exercices.
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3.4. Classical time and space discretization techniques -- 3.5. Stability and accuracy analysis -- 3.6. Taylor-Galerkin Methods -- 3.7. An introduction to monotonicity-preserving schemes -- 3.8. Least-squares-based spatial discretization -- 3.9. The discontinuous Galerkin method -- 3.10. Space-time formulations -- 3.11. Applications and solved exercises -- 4. Compressible Flow Problems -- 4.1. Introduction -- 4.2. Nonlinear hyperbolic equations -- 4.3. The Euler equations -- 4.4. Spatial discretization techniques -- 4.5. Numerical treatment of shocks -- 4.6. Nearly incompressible flows -- 4.7. Fluid-structure interaction -- 4.8. Solved exercises -- 8
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1. Introduction and preliminaries -- 1.1. Finite elements in fluid dynamics -- 1.2. Subjects covered -- 1.3. Kinematical descriptions of the flow field -- 1.4. The basic conservation equations -- 1.5. Basic ingredients of the finite element method -- 2. Steady transport problems -- 2.1. Problem statement -- 2.2. Galerkin approximation -- 2.3. Early Petrov-Galerkin methods -- 2.4. Stabilization techniques -- 2.5. Other stabilization techniques and new trends -- 2.6. Applications and solved exercises -- 3. Unsteady convective transport -- 3.1. Introduction -- 3.2. Problem statement -- 3.3. The method of characteristics -- 8