Author | Girault, Vivette. author |
---|---|
Title | Finite Element Methods for Navier-Stokes Equations [electronic resource] : Theory and Algorithms / by Vivette Girault, Pierre-Arnaud Raviart |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-61623-5 |
Descript | X, 376 p. online resource |
I. Mathematical Foundation of the Stokes Problem -- ยง 1. Generalities on Some Elliptic Boundary Value Problems -- ยง2. Function Spaces for the Stokes Problem -- ยง 3. A Decomposition of Vector Fields -- ยง4. Analysis of an Abstract Variational Problem -- ยง5. The Stokes Equations -- Appendix A. Results of Standard Finite Element Approximation -- II. Numerical Solution of the Stokes Problem in the Primitive Variables -- ยง1. General Approximation -- ยง 2. Simplicial Finite Element Methods Using Discontinuous Pressures -- ยง 3. Quadrilateral Finite Element Methods Using Discontinuous Pressures -- ยง4. Continuous Approximation of the Pressure -- III. Incompressible Mixed Finite Element Methods for Solving the Stokes Problem -- ยง1. Mixed Approximation of an Abstract Problem -- ยง2. The โStream Function-Vorticity-Pressureโ Method for the Stokes Problem in Two Dimensions -- ยง 3. Further Topics on the โStream Function-Vorticity-Pressureโ Scheme -- ยง 4. A โStream Function-Gradient of Velocity Tensorโ Method in Two Dimensions -- ยง 5. A โVector Potential-Vorticityโ Scheme in Three Dimensions -- IV. Theory and Approximation of the Navier-Stokes Problem -- ยง 1. A Class of Nonlinear Problems -- ยง2. Theory of the Steady-State Navier-Stokes Equations -- ยง 3. Approximation of Branches of Nonsingular Solutions -- ยง4. Numerical Analysis of Centered Finite Element Schemes -- ยง 5. Numerical Analysis of Upwind Schemes -- ยง6. Numerical Algorithms -- References -- Index of Mathematical Symbols