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Implementation of Finite Element Methods for Navier-Stokes Equations

In structure mechanics analysis, finite element methods are now well estab­ lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numeric...

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Bibliographic Details
Main Author: Thomasset, F.
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 1981, 1981
Edition:1st ed. 1981
Series:Scientific Computation
Subjects:
Continuum Mechanics
Mathematical Physics
Theoretical, Mathematical And Computational Physics
Mathematical Methods In Physics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Notations
  • 1. Elliptic Equations of Order 2: Some Standard Finite Element Methods
  • 1.1. A 1-Dimensional Model Problem: The Basic Notions
  • 1.2. A 2-Dimensional Problem
  • 1.3. The Finite Element Equations
  • 1.4. Standard Examples of Finite Element Methods
  • 1.5. Mixed Formulation and Mixed Finite Element Methods for Elliptic Equations
  • 2. Upwind Finite Element Schemes
  • 2.1. Upwind Finite Differences
  • 2.2. Modified Weighted Residual (MWR)
  • 2.3. Reduced Integration of the Advection Term
  • 2.4. Computation of Directional Derivatives at the Nodes
  • 2.5. Discontinuous Finite Elements and Mixed Interpolation
  • 2.6. The Method of Characteristics in Finite Elements
  • 2.7. Peturbation of the Advective Term: Bredif (1980)
  • 2.8. Some Numerical Tests and Further Comments
  • 3. Numerical Solution of Stokes Equations
  • 3.1. Introduction
  • 3.2. Velocity—Pressure Formulations: Discontinuous Approximations of the Pressure
  • 3.3. Velocity—Pressure Formulations: Continuous Approximation of the Pressure and Velocity
  • 3.4. Vorticity—Pressure—Velocity Formulations: Discontinuous Approximations of Pressure and Velocity
  • 3.5. Vorticity Stream-Function Formulation: Decompositions of the Biharmonic Problem
  • 4. Navier-Stokes Equations: Accuracy Assessments and Numerical Results
  • 4.1. Remarks on the Formulation
  • 4.2. A review of the Different Methods
  • 4.3. Some Numerical Tests
  • 5. Computational Problems and Bookkeeping
  • 5.1. Mesh Generation
  • 5.2. Solution of the Nonlinear Problems
  • 5.3. Iterative and Direct Solvers of Linear Equations
  • Appendix 2. Numerical Illustration
  • Three Dimensional Case
  • References

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