The Resource NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
Resource Information
The item NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of MissouriSt. Louis Libraries.
This item is available to borrow from 1 library branch.
 Summary
 This volume deals with the classical NavierStokes system of equations governing the planar flow of incompressible, viscid fluid. It is a firstofitskind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "doubledriven cavity". A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics
 Language
 eng
 Extent
 1 online resource (xii, 302 pages)
 Contents

 pt. I. Basic theory. 1. Introduction. 1.1. Functional notation
 2. Existence and uniqueness of smooth solutions. 2.1. The linear convectiondiffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2
 3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3
 4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4
 5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5
 6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6
 A. Some theorems from functional analysis. A.1. The CalderónZygmund theorem. A.2. Young's and the HardyLittlewoodSobolev inequalities. A.3. The RieszThorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel
 pt. II. Approximate solutions. 7. Introduction
 8. Notation. 8.1. Onedimensional discrete setting. 8.2. Twodimensional discrete setting
 9. Finite difference approximation to secondorder boundaryvalue problems. 9.1. The principle of finite difference schemes. 9.2. The threepoint Laplacian. 9.3. Matrix representation of the threepoint Laplacian. 9.4. Notes for chapter 9
 10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The threepoint biharmonic operator. 10.4. Accuracy of the threepoint biharmonic operator. 10.5. Coercivity and stability properties of the threepoint biharmonic operator. 10.6. Matrix representation of the threepoint biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10
 11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11
 12. Compact approximation of the NavierStokes equations in streamfunction formulation. 12.1. The NavierStokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12
 B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation
 13. Fully discrete approximation of the NavierStokes equations. 13.1. Fourthorder approximation in space. 13.2. A timestepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13
 14. Numerical simulations of the driven cavity problem. 14.1. Secondorder scheme for the driven cavity problem. 14.2. Fourthorder scheme for the driven cavity problem. 14.3. Doubledriven cavity problem. 14.4. Notes for chapter 14
 Isbn
 9781848162761
 Label
 NavierStokes equations in planar domains
 Title
 NavierStokes equations in planar domains
 Statement of responsibility
 Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
 Language
 eng
 Summary
 This volume deals with the classical NavierStokes system of equations governing the planar flow of incompressible, viscid fluid. It is a firstofitskind book, devoted to all aspects of the study of such flows, ranging from theoretical to numerical, including detailed accounts of classical test problems such as "driven cavity" and "doubledriven cavity". A comprehensive treatment of the mathematical theory developed in the last 15 years is elaborated, heretofore never presented in other books. It gives a detailed account of the modern compact schemes based on a "pure streamfunction" approach. In particular, a complete proof of convergence is given for the full nonlinear problem. This volume aims to present a variety of numerical test problems. It is therefore well positioned as a reference for both theoretical and applied mathematicians, as well as a text that can be used by graduate students pursuing studies in (pure or applied) mathematics, fluid dynamics and mathematical physics
 Cataloging source
 WSPC
 http://library.link/vocab/creatorDate
 1948
 http://library.link/vocab/creatorName
 BenArtzi, Matania
 Dewey number
 532.05201515353
 Illustrations
 illustrations
 Index
 index present
 LC call number
 QA374
 LC item number
 .B46 2013
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorDate
 1961
 http://library.link/vocab/relatedWorkOrContributorName

 Croisille, JeanPierre
 Fishelov, Dalia
 World Scientific (Firm)
 http://library.link/vocab/subjectName

 NavierStokes equations
 SCIENCE
 NavierStokes equations
 Label
 NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
 Bibliography note
 Includes bibliographical references (pages 287297) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 black and white
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 pt. I. Basic theory. 1. Introduction. 1.1. Functional notation  2. Existence and uniqueness of smooth solutions. 2.1. The linear convectiondiffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2  3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3  4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4  5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5  6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6  A. Some theorems from functional analysis. A.1. The CalderónZygmund theorem. A.2. Young's and the HardyLittlewoodSobolev inequalities. A.3. The RieszThorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel  pt. II. Approximate solutions. 7. Introduction  8. Notation. 8.1. Onedimensional discrete setting. 8.2. Twodimensional discrete setting  9. Finite difference approximation to secondorder boundaryvalue problems. 9.1. The principle of finite difference schemes. 9.2. The threepoint Laplacian. 9.3. Matrix representation of the threepoint Laplacian. 9.4. Notes for chapter 9  10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The threepoint biharmonic operator. 10.4. Accuracy of the threepoint biharmonic operator. 10.5. Coercivity and stability properties of the threepoint biharmonic operator. 10.6. Matrix representation of the threepoint biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10  11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11  12. Compact approximation of the NavierStokes equations in streamfunction formulation. 12.1. The NavierStokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12  B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation  13. Fully discrete approximation of the NavierStokes equations. 13.1. Fourthorder approximation in space. 13.2. A timestepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13  14. Numerical simulations of the driven cavity problem. 14.1. Secondorder scheme for the driven cavity problem. 14.2. Fourthorder scheme for the driven cavity problem. 14.3. Doubledriven cavity problem. 14.4. Notes for chapter 14
 Control code
 844311053
 Dimensions
 other
 Extent
 1 online resource (xii, 302 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781848162761
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations
 Quality assurance targets
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)844311053
 Label
 NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
 Bibliography note
 Includes bibliographical references (pages 287297) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 black and white
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 pt. I. Basic theory. 1. Introduction. 1.1. Functional notation  2. Existence and uniqueness of smooth solutions. 2.1. The linear convectiondiffusion equation. 2.2. Proof of theorem 2.1. 2.3. Existence and uniqueness in Hölder spaces. 2.4. Notes for chapter 2  3. Estimates for smooth solutions. 3.1. Estimates involving [symbol]. 3.2. Estimates involving [symbol]. 3.3. Estimating derivatives. 3.4. Notes for chapter 3  4. Extension of the solution operator. 4.1. An intermediate extension. 4.2. Extension to initial vorticity in [symbol]. 4.3. Notes for chapter 4  5. Measures as initial data. 5.1. Uniqueness for general initial measures. 5.2. Notes for chapter 5  6. Asymptotic behavior for large time. 6.1. Decay estimates for large time. 6.2. Initial data with stronger spatial decay. 6.3. Stability of steady states. 6.4. Notes for chapter 6  A. Some theorems from functional analysis. A.1. The CalderónZygmund theorem. A.2. Young's and the HardyLittlewoodSobolev inequalities. A.3. The RieszThorin interpolation theorem. A.4. Finite Borel measures in [symbol] and the heat kernel  pt. II. Approximate solutions. 7. Introduction  8. Notation. 8.1. Onedimensional discrete setting. 8.2. Twodimensional discrete setting  9. Finite difference approximation to secondorder boundaryvalue problems. 9.1. The principle of finite difference schemes. 9.2. The threepoint Laplacian. 9.3. Matrix representation of the threepoint Laplacian. 9.4. Notes for chapter 9  10. From Hermitian derivative to the compact discrete biharmonic operator. 10.1. The Hermitian derivative operator. 10.2. A finite element approach to the Hermitian derivative. 10.3. The threepoint biharmonic operator. 10.4. Accuracy of the threepoint biharmonic operator. 10.5. Coercivity and stability properties of the threepoint biharmonic operator. 10.6. Matrix representation of the threepoint biharmonic operator. 10.7. Convergence analysis using the matrix representation. 10.8. Notes for chapter 10  11. Polynomial approach to the discrete biharmonic operator. 11.1. The biharmonic problem in a rectangle. 11.2. The biharmonic problem in an irregular domain. 11.3. Notes for chapter 11  12. Compact approximation of the NavierStokes equations in streamfunction formulation. 12.1. The NavierStokes equations in streamfunction formulation. 12.2. Discretizing the streamfunction equation. 12.3. Convergence of the scheme. 12.4. Notes for chapter 12  B. Eigenfunction approach for [symbol]. B.1. Some basic properties of the equation. B.2. The discrete approximation  13. Fully discrete approximation of the NavierStokes equations. 13.1. Fourthorder approximation in space. 13.2. A timestepping discrete scheme. 13.3. Numerical results. 13.4. Notes for chapter 13  14. Numerical simulations of the driven cavity problem. 14.1. Secondorder scheme for the driven cavity problem. 14.2. Fourthorder scheme for the driven cavity problem. 14.3. Doubledriven cavity problem. 14.4. Notes for chapter 14
 Control code
 844311053
 Dimensions
 other
 Extent
 1 online resource (xii, 302 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781848162761
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other physical details
 illustrations
 Quality assurance targets
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)844311053
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.umsl.edu/portal/NavierStokesequationsinplanardomains/nk8KOOvbCX4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.umsl.edu/portal/NavierStokesequationsinplanardomains/nk8KOOvbCX4/">NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.umsl.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.umsl.edu/">University of MissouriSt. Louis Libraries</a></span></span></span></span></div>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data  Experimental
Data Citation of the Item NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov
Copy and paste the following RDF/HTML data fragment to cite this resource
<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.umsl.edu/portal/NavierStokesequationsinplanardomains/nk8KOOvbCX4/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.umsl.edu/portal/NavierStokesequationsinplanardomains/nk8KOOvbCX4/">NavierStokes equations in planar domains, Matania BenArtzi, JeanPierre Croisille, Dalia Fishelov</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.umsl.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.umsl.edu/">University of MissouriSt. Louis Libraries</a></span></span></span></span></div>