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Lagrangian approximations and weak solutions of the Navier-Stokes equations

100%

Varnhorn W.

Banach Center Publications

2008

tom 81

nr 1

515-532

The motion of a viscous incompressible fluid flow in bounded domains with a smooth boundary can be described by the nonlinear Navier-Stokes equations. This description corresponds to the so-called Eulerian approach. We develop a new approximation method for the Navier-Stokes equations in both the stationary and the non-stationary case by a suitable coupling of the Eulerian and the Lagrangian representation of the flow, where the latter is defined by the trajectories of the particles of the fluid. The method leads to a sequence of uniquely determined approximate solutions with a high degree of regularity containing a convergent subsequence with limit function v such that v is a weak solution of the Navier-Stokes equations.

Finite differences and boundary element methods for non-stationary viscous incompressible flow

100%

Varnhorn W.

Banach Center Publications

1994

tom 29

nr 1

135-154

We consider an implicit fractional step procedure for the time discretization of the non-stationary Stokes equations in smoothly bounded domains of ℝ³. We prove optimal convergence properties uniformly in time in a scale of Sobolev spaces, under a certain regularity of the solution. We develop a representation for the solution of the discretized equations in the form of potentials and the uniquely determined solution of some system of boundary integral equations. For the numerical computation of the potentials and the solution of the boundary integral equations a boundary element method of collocation type is carried out.

Ograniczanie wyników

2 Banach Center Publications

2 Varnhorn W.

1 2008

1 1994

Wyniki wyszukiwania

Lagrangian approximations and weak solutions of the Navier-Stokes equations

Finite differences and boundary element methods for non-stationary viscous incompressible flow