Convergence of Numerical Approximations for the Navier-Stokes Equations with Boundaries [microform] : Vorticity and Primitive Formulations PDF Download

Author: Wetton, Brian Thomas Robinson
Publisher: Ann Arbor, Mich. : University Microfilms International
ISBN:
Category :
Languages : en
Pages : 188

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Author: Brian Thomas Robinson Wetton
Publisher:
ISBN:
Category :
Languages : en
Pages : 188

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Author: Alexandre Jo©·el Chorin
Publisher:
ISBN:
Category : Differential equations
Languages : en
Pages : 40

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Author: Alfio Quarteroni
Publisher: Springer Science & Business Media
ISBN: 3540852689
Category : Mathematics
Languages : en
Pages : 551

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Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).

Author: John G. Heywood
Publisher: Springer
ISBN: 3540471413
Category : Mathematics
Languages : en
Pages : 245

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These proceedings contain original (refereed) research articles by specialists from many countries, on a wide variety of aspects of Navier-Stokes equations. Additionally, 2 survey articles intended for a general readership are included: one surveys the present state of the subject via open problems, and the other deals with the interplay between theory and numerical analysis.

Author: Long'an Ying
Publisher: World Scientific
ISBN: 9812772561
Category : Mathematics
Languages : en
Pages : 282

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Preface -- 1. Exterior problems of partial differential equations. 1.1. Harmonic equation-potential theory. 1.2. Poisson equations. 1.3. Poisson equations-variational formulation. 1.4. Helmholtz equations. 1.5. Linear elasticity. 1.6. Bi-harmonic equations. 1.7. Steady Navier-Stokes equations-linearized problems. 1.8. Steady Navier-Stokes equations. 1.9. Heat equation. 1.10. Wave equation. 1.11. Maxwell equations. 1.12. Darwin model -- 2. Boundary element method. 2.1. Some typical domains. 2.2. General domains. 2.3. Subdivision of the domain. 2.4. Dirichlet to Neǔmann operator. 2.5. Finite part of divergent integrals. 2.6. Numerical approximation. 2.7. Error estimates. 2.8. Domain decomposition. 2.9. Boundary perturbation -- 3. Infinite element method. 3.1. Harmonic equation-two dimensional problems. 3.2. General elements. 3.3. Harmonic equation-three dimensional problems. 3.4. Inhomogeneous equations. 3.5. Plane elasticity. 3.6. Bi-harmonic equations. 3.7. Stokes equation. 3.8. Darwin model. 3.9. Elliptic equations with variable coefficients. 3.10. Convergence -- 4. Artificial boundary conditions. 4.1. Absorbing boundary conditions. 4.2. Some approximations. 4.3. Bayliss-Turkel radiation boundary conditions. 4.4. A lower order absorbing boundary condition. 4.5. Liao extrapolation in space and time. 4.6. Maxwell equations. 4.7. Finite difference schemes. 4.8. Stationary Navier-Stokes equations -- 5. Perfectly matched layer method. 5.1. Wave equations. 5.2. Bérenger's perfectly matched layers. 5.3. Stability analysis. 5.4. Uniaxial perfectly matched layers. 5.5. Maxwell equations. 5.6. Helmholtz equations -- 6. Spectral method. 6.1. Introduction. 6.2. Orthogonal systems of polynomials. 6.3. Laguerre spectral methods. 6.4. Jacobi spectral methods. 6.5. Rational and irrational spectral methods. 6.6. Error estimates

Author: Wolfgang Hackbusch
Publisher: Springer-Verlag
ISBN: 3663140040
Category : Technology & Engineering
Languages : de
Pages : 174

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Author: R. Rautmann
Publisher: Springer
ISBN: 3540385509
Category : Mathematics
Languages : en
Pages : 602

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Author: John G. Heywood
Publisher: Springer
ISBN: 3540474986
Category : Science
Languages : en
Pages : 329

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V.A. Solonnikov, A. Tani: Evolution free boundary problem for equations of motion of viscous compressible barotropic liquid.- W. Borchers, T. Miyakawa:On some coercive estimates for the Stokes problem in unbounded domains.- R. Farwig, H. Sohr: An approach to resolvent estimates for the Stokes equations in L(q)-spaces.- R. Rannacher: On Chorin's projection method for the incompressible Navier-Stokes equations.- E. S}li, A. Ware: Analysis of the spectral Lagrange-Galerkin method for the Navier-Stokes equations.- G. Grubb: Initial value problems for the Navier-Stokes equations with Neumann conditions.- B.J. Schmitt, W. v.Wahl: Decomposition of solenoidal fields into poloidal fields, toroidal fields and the mean flow. Applications to the Boussinesq-equations.- O. Walsh: Eddy solutions of the Navier-Stokesequations.- W. Xie: On a three-norm inequality for the Stokes operator in nonsmooth domains.

Author: Adélia Sequeira
Publisher: Springer Science & Business Media
ISBN: 1489914153
Category : Science
Languages : en
Pages : 393

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Book Description
This volume contains the Proceedings of the Third International Conference on Navier-Stokes Equations and Related Nonlinear Problems. The conference was held in Funchal (Madeira, Portugal), on May 21-27, 1994. In addition to the editor, the organizers were Carlos Albuquerque (FC, University of Lisbon), Casimiro Silva (University of Madeira) and Juha Videman (1ST, Technical University of Lisbon). This meeting, following two other successful events of similar type held in Thurnau (Germany) in 1992 and in Cento (Italy) in 1993, brought together, to the majestically beautiful island of Madeira, more than 60 specialists from all around the world, of which about two thirds were invited lecturers. The main interest of the meeting was focused on the mathematical analysis of nonlinear phenomena in fluid mechanics. During the conference, we noticed that this area seems to provide, today more than ever, challenging and increasingly important problems motivating the research of both theoretical and numerical analysts. This volume collects 32 articles selected from the invited lectures and contributed papers given during the conference. The main topics covered include: Flows in Unbounded Domains; Flows in Bounded Domains; Compressible Fluids; Free Boundary Problems; Non-Newtonian Fluids; Related Problems and Numerical Approximations. The contributions present original results or new surveys on recent developments, giving directions for future research. I express my gratitude to all the authors and I am glad to recognize the scientific level and the actual interest of the articles.