Finite Element Methods and Navier-Stokes Equations (Mathematics and Its Applications, 22) - gebonden uitgave, pocketboek

EAN (ISBN-13): 9789027721488
ISBN (ISBN-10): 9027721483
Gebonden uitgave
Verschijningsjaar: 1986
Uitgever: Springer
504 Bladzijden
Gewicht: 0,912 kg
Taal: eng/Englisch

Boek bevindt zich in het datenbestand sinds 2007-06-12T21:47:34+02:00 (Amsterdam)
Detailpagina laatst gewijzigd op 2024-01-24T05:33:11+01:00 (Amsterdam)
ISBN/EAN: 9027721483

ISBN - alternatieve schrijfwijzen:
90-277-2148-3, 978-90-277-2148-8
alternatieve schrijfwijzen en verwante zoekwoorden:
Auteur van het boek: cuvelier, segal
Titel van het boek: ons element, finite element methods navier stokes equations, finite mathematics, finite element methods applications, cuvelier, using finite element methods

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Gegevens van de uitgever

Auteur: C. Cuvelier; A. Segal; A.A. van Steenhoven
Titel: Mathematics and Its Applications; Finite Element Methods and Navier-Stokes Equations
Uitgeverij: Springer; Springer Netherland
504 Bladzijden
Verschijningsjaar: 1986-03-31
Dordrecht; NL
Gewicht: 1,940 kg
Taal: Engels
139,09 € (DE)
142,99 € (AT)
143,00 CHF (CH)
Not available, publisher indicates OP

BB; Book; Hardcover, Softcover / Informatik, EDV/Informatik; Theoretische Informatik; CON_D014; C; Numeric Computing; Mathematics and Statistics; EA

I Introduction to the Finite Element Method.- 1 Examples of partial differential equations.- 1.1 Classification of PDEs.- 1.2 Laplace and Poisson equation.- 1.3 Steady state convection-diffusion equation.- 1.4 Time dependent convection-diffusion equation.- 1.5 Reynolds equation.- 1.6 Equations of fluid dynamics; Navier-Stokes equations.- 1.7 Equations of linear elasticity.- 1.8 Comments.- 2 Finite difference schemes for Poisson equation and convection-diffusion equation.- 2.1 1D Poisson equation with Dirichlet boundary conditions.- 2.2 1D Poisson equation with other type of boundary conditions.- 2.2.1 Mixed homogeneous Dirichlet-Neumann boundary conditions.- 2.2.2 Non-homogeneous Dirichlet boundary conditions.- 2.2.3 Non-homogeneous Neumann boundary conditions.- 2.2.4 Non-homogeneous Robbins boundary conditions.- 2.3 2D Poisson equation with Dirichlet boundary conditions.- 2.4 Boundary conditions, geometry and variable coefficients in 2D.- 2.4.1 Boundary conditions.- 2.4.2 Geometry.- 2.4.3 Variable coefficients.- 2.5 Comments.- 2.6 Convection-diffusion equation.- 3 The finite element method.- 3.1 Extremal problem; Euler-Lagrange equation.- 3.2 Extremal formulation of the Poisson equation.- 3.2.1 1D case.- 3.2.2 2D case.- 3.2.3 Various types of boundary conditions.- 3.3 Comments.- 3.4 The Ritz method.- 3.5 The FEM.- 3.5.1 Definition.- 3.5.2 1D Poisson equation.- 3.6 The Galerkin method.- 3.6.1 General procedure.- 3.6.2 1D Poisson equation; homogeneous boundary conditions.- 3.6.3 1D Poisson equation; non-homogeneous boundary conditions.- 3.6.4 2D problem.- 3.7 Comments.- 4 Construction of finite elements.- 4.1 Linear, quadratic and cubic basis functions in 1D.- 4.2 Triangular basis functions in 2D.- 4.2.1 Barycentric coordinates.- 4.2.2 Linear finite element.- 4.2.3 Linear finite element (with reduced continuity).- 4.2.4 Quadratic finite element.- 4.2.5 Extended quadratic finite element.- 4.3 Triangular basis functions in 3D.- 4.3.1 Barycentric coordinates.- 4.3.2 Linear finite element.- 4.3.3 Linear finite element (with reduced continuity).- 4.4 Coordinate and element transformation.- 4.5 Quadrilateral finite element.- 4.5.1 Bilinear finite element.- 4.5.2 Biquadratic finite element.- 4.6 Hexahedral finite elements.- 4.6.1 Trilinear finite element.- 4.6.2 Triquadratic finite element.- 5 Practical aspects of the finite element method.- 5.1 Finite element assembly algorithm.- 5.2 1D Poisson equation; quadratic finite elements.- 5.3 2D Poisson equation; linear and quadratic triangular elements.- 5.3.1 Linear finite element.- 5.3.2 Quadratic finite element.- 5.4 Numerical integration formulas.- 5.4.1 Numerical integration on intervals, triangles and tetrahedra.- 5.4.2 Numerical integration on quadrilaterals and hexahedra.- 5.5 Accuracy aspects of the FEM.- 5.6 Solution methods for systems of (non-)linear equations.- 5.6.1 Direct methods to solve systems of linear equations.- 5.6.2 Iterative methods for the solution of systems of linear equations.- 5.6.3 Linearization techniques for systems of nonlinear equations.- 5.6.3.1 Picard iteration.- 5.6.3.2 Newton’s method.- 5.6.3.3 The quasi-Newton method.- II Application of the Finite Element Method to the Navier-Stokes Equations.- 6 Alternative formulations of Navier-Stokes equations.- 6.1 The basic equations of fluid dynamics.- 6.2 Alternative formulations.- 6.3 Initial and boundary conditions.- 6.3.1 Introduction.- 6.3.2 Velocity-pressure formulation.- 6.3.3 Stream function-vorticity formulation.- 6.3.4 Some practical remarks concerning the boundary conditions.- 6.4 Evaluation of the various formulations.- 7 The integrated method.- 7.1 General approach.- 7.2 Practical elaboration.- 7.2.1 Complicated boundary conditions.- 7.2.2 Necessary conditions for the elements.- 7.2.3 Examples of admissible elements.- 7.2.3.1 Introduction.- 7.2.3.2 Triangular elements (Taylor-Hood (1973)).- 7.2.3.3 Triangular elements (Crouzeix-Raviart (1973)).- 7.2.3.4 Quadrilateral elements.- 7.2.3.5 3D elements.- 7.2.4 The structure of the equations.- 7.3 The Navier-Stokes equations.- 7.3.1 Introduction.- 7.3.2 The Picard iteration.- 7.3.3 Newton and quasi-Newton methods.- 7.3.4 The structure of the system of equations.- 7.4 Evaluation of the integrated method.- 8 The penalty function method.- 8.1 General approach.- 8.2 Alternative formulations of the penalty function method.- 8.2.1 Minimization formulation.- 8.2.2 The continuous penalty function method.- 8.2.3 Iterative penalty function method.- 8.3 Practical consequences.- 8.3.1 Element conditions.- 8.3.2 The modified P2+-P1 Crouzeix-Raviart element.- 8.3.2.1 Introduction.- 8.3.2.2 Elimination of the velocities in the centroid.- 8.3.2.3 Elimination of the pressure derivatives.- 8.3.2.4 Construction of matrices.- 8.3.2.5 Concluding remarks.- 8.3.3 The structure of the equations.- 8.4 Evaluation of the penalty function method.- 9 Divergence-free elements.- 9.1 General approach.- 9.2 The construction of divergence-free basis functions for 2D elements.- 9.2.1 Introduction.- 9.2.2 The non-conforming Crouzeix-Raviart element.- 9.2.3 The modified P2+-P1 Crouzeix-Raviart element.- 9.2.4 The Q2-P1 9-node quadrilateral.- 9.2.5 Boundary conditions.- 9.2.6 The structure of the system of equations.- 9.2.7 The implementation of boundary conditions of the type ? equals unknown constant.- 9.3 The construction of divergence-free basis functions for 3D elements.- 9.3.1 Introduction.- 9.3.2 A non-conforming Crouzeix-Raviart element in IR3.- 9.3.3 The construction of a divergence-free basis.- 9.4 Evaluation of the solenoidal method.- 10 The instationary Navier-Stokes equations.- 10.1 General approach.- 10.2 The numerical solution of systems of ordinary differential equations.- 10.2.1 Introduction.- 10.2.2 Stability of the ?-method.- 10.3 The solution of the systems of ordinary differential equations resulting from the Galerkin method applied to the Navier-Stokes equations.- 10.3.1 The penalty function method and artificial compressibility methods.- 10.3.2 Divergence-free elements.- 10.3.3 The pressure-correction method.- 10.4 Streamline upwinding.- III Theoretical Aspects of the Finite Element Method.- 11 Second order elliptic PDEs.- 11.1 Dirichlet problem for the Laplace operator.- 11.2 Neumann problem for the Laplace operator.- 11.3 General variational formulation; existence, uniqueness.- 11.4 Examples.- 11.5 (Navier-) Stokes equations.- 11.6 Regularity of the solution of the variational problem.- 12 Finite element approximations of variational problems.- 12.1 Internal approximation of Hilbert spaces.- 12.2 Discretized variational problem.- 12.3 Finite element approximations of Sobolev spaces.- 12.3.1 Definition of finite element.- 12.3.2 Linear finite element approximation of L2(?).- 12.3.3 Linear finite element approximation of H01(?).- 12.3.4 Quadratic finite element approximation of H01(?).- 12.3.5 Linear finite element approximation of H1(?).- 12.3.6 Finite element approximation of V.- 12.4 Interpretation of the discretized variational problem.- 12.4.1 Dirichlet-Neumann problem for the Laplace operator.- 12.4.2 Stokes problem.- 13 Error analysis of the FEM.- 13.1 H1 and L2 error estimates.- 13.2 Numerical integration.- 14 Mixed Finite Element Methods.- IV Current Research Topics.- 15 Capillary free boundaries governed by the Navier-Stokes equations.- 15.1 Mathematical model.- 15.2 Normal stress iterative method.- 15.3 Newton’s method for free boundaries.- 16 Non-Isothermal flows.- 16.1 Mathematical model.- 16.2 Numerical treatment.- 17 Turbulence.- 17.1 Mathematical models.- 17.2 Numerical treatment.- 18 Non-Newtonian fluids.- 18.1 Mathematical models.- 18.2 Numerical treatment.