Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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FINITE ELEMENT ANALYSIS FOR A MIXED LAGRANGIAN FORMULATION OF INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

  • Kim, Hong-Chul (Department of Mathematics Kangnung National University )
  • Published : 1997.02.01
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Abstract

This paper is concerned with a mixed Lagrangian formulation of the wiscous, stationary, incompressible Navier-Stokes equations $$ (1.1) -\nu\Delta u + (u \cdot \nabla)u + \nabla_p = f in \Omega $$ and $$ (1.2) \nubla \cdot u = 0 in \Omega $$ along with inhomogeneous Dirichlet boundary conditions on a portion of the boundary $$ (1.3) u = ^{0 on \Gamma_0 _{g on \Gamma_g, $$ where $\Omega$ is a bounded open domain in $R^d, d = 2 or 3$, or with a boundary $\Gamma = \partial\Omega$, which is composed of two disjoint parts $\Gamma_0$ and $\Gamma_g$.

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References

  1. Sobolev spaces R. Adams
  2. Numer. Math. v.20 The finite method with Lagrange multipliers I. Babuska
  3. Math. Comp. v.30 Higher order approximations to the boundary conditions for the finite element method J. Blair
  4. Math. Comp. v.37 The Lagrange multiplier method for Dirichlet's problem J. Bramble
  5. Numer. Math. v.36 Finite-dimensional approximation of nonlinear problems. PartⅠ: Branches of nonsingular solutions F. Brezzi;P.-A. Raviart
  6. The finite element method for elliptic problems P. Ciarlet
  7. Theory and algorithms Finite element methods for Navier-Stokes equations V. Girault;P.-A. Raviart
  8. Elliptic problems in non-smooth domains P. Grisvard
  9. Math. Comp. v.57 Analysis and finite element approximation of optimal control problems for the stationary Navier-Stokes equations with distributed and Neumann controls M. Gunzburger;L. Hou;T. Svobodny
  10. Incompressible Computational Fluid Dynamics Optimal control and optimization of viscous incompressible flows M. Gunzburger;L. Hou;T. Svobodny;M. Gunzburger(ed.);R.A. Nicolaids(ed.)
  11. SIAM J. Numer. Anal. v.29 Treating inhomogeneous essential boundary conditions in finite element methods and the calculation of boundary stresses M. Gunzburger;L. Hou
  12. Existence of an optimal solution of a shape control problem for the stationary Navier-Stokes equations M. Gunzburger;H. Kim
  13. Sensitivity analysis of a shape control problem for the stationary Navier-Stokes equations M. Gunzburger;H. Kim
  14. Math. Comp. v.37 The finite element method with Lagrange multipliers for domains with corners J. Pitkaranta
  15. Navier-Stokes equations: Theory and numerical analysis R. Temam
  16. RAIRO Anal. Numer. v.18 Error estimates for a mixed finite element approximations of the Stokes equations R. Verfurth
  17. Numer. Math. v.50 Finite element approximation of incompressible Navier-Stokes equations with slip boundary condition R. Verfurth