Wyniki wyszukiwania - BazTech

1

On fractional vectorial calculus

Ortigueira M. D., Machado J. T. M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

|

2018

|

Vol. 66, nr 4

389--402

EN

This paper reviews the fractional vectorial differential operators proposed previously and introduces the fractional versions of the classic Green’s, Stokes’, and Ostrogradski-Gauss’s integral theorems. The suitability of fractional derivatives for sciences and the Laplacian definition are also discussed.

2

The Lagrange multiplier and the stationary Stokes equations

Ożański W. S.

Journal of Applied Analysis

|

2017

|

Vol. 23, nr 2

137--140

EN

We briefly discuss the notion of the Lagrange multiplier for a linear constraint in the Hilbert space setting, and we prove that the pressure p appearing in the stationary Stokes equations is the Lagrange multiplier of the constraint div u = 0.

3

The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation

Khapalov A.

International Journal of Applied Mathematics and Computer Science

|

2013

|

Vol. 23, no. 2

277--290

EN

We introduce and investigate the well-posedness of a model describing the self-propelled motion of a small abstract swimmer in the 3-D incompressible fluid governed by the nonstationary Stokes equation, typically associated with low Reynolds numbers. It is assumed that the swimmer’s body consists of finitely many subsequently connected parts, identified with the fluid they occupy, linked by rotational and elastic Hooke forces. Models like this are of interest in biological and engineering applications dealing with the study and design of propulsion systems in fluids.

4

Addendum to “The well-posedness of a swimming model in the 3-D incompressible fluid governed by the nonstationary Stokes equation”

Khapalov A.

International Journal of Applied Mathematics and Computer Science

|

2013

|

Vol. 23, no. 4

905--906

EN

In this addendum we address some unintentional omission in the description of the swimming model in our recent paper (Khapalov, 2013).

5

Effects of magnetic field on stokes flow due to an oscillating wall under the fluid slip condition

Poria S.

International Journal of Applied Mechanics and Engineering

|

2008

|

Vol. 13, no 3

847-853

EN

In this paper we have studied the motion of an incompressible viscous conducting fluid about an harmonically oscillating vertical wall under fluid slip boundary condition at the wall and subjected to a uniform weak transverse magnetic filed. Effects of variations of the magnetic field and the slip parameter on the evolution of the velocity filed and shear stress are determined and discussed.

6

Finite element error analysis for state-constrained optimal control of the Stokes equations

Los Reyes J. C. de, Meyer C., Vexler B.

Control and Cybernetics

|

2008

|

Vol. 37, no 2

251-284

EN

An optimal control problem for 2d and 3d Stokes equations is investigated with pointwise inequality constraints on the state and the control. The paper is concerned with the full discretization of the control problem allowing for different types of discretization of both the control and the state. For instance, piecewise linear and continuous approximations of the control are included in the present theory. Under certain assumptions on the L∞-error of the finite element discretization of the state, error estimates for the control are derived which can be seen to be optimal since their order of convergence coincides with the one of the interpolation error. The assumptions of the L∞-finite-eleinent-error can be verified for different numerical settings. Finally the results of two numerical experiments are presented.