TY - JOUR

T1 - A Boundary Value Problem for an Overdetermined Steady System in Two-Velocity Hydrodynamics

AU - Urev, M. V.

AU - Imomnazarov, Kh Kh

AU - Tang, Jian Gang

PY - 2017/10/1

Y1 - 2017/10/1

N2 - In this paper, a two-velocity steady hydrodynamic system with a single pressure and inhomogeneous divergent and boundary conditions for two velocities is investigated. This system is overdetermined. By changing the sought-for functions, the problem is reduced to a homogeneous one. The resulting system is solved by consecutively solving two boundary value problems: a Stokes problem for one velocity and the pressure and an overdetermined system for the other velocity. Generalized statements of these problems and their discrete approximations using a finite element method are presented. A new regularization method is used to solve the overdetermined problem.

AB - In this paper, a two-velocity steady hydrodynamic system with a single pressure and inhomogeneous divergent and boundary conditions for two velocities is investigated. This system is overdetermined. By changing the sought-for functions, the problem is reduced to a homogeneous one. The resulting system is solved by consecutively solving two boundary value problems: a Stokes problem for one velocity and the pressure and an overdetermined system for the other velocity. Generalized statements of these problems and their discrete approximations using a finite element method are presented. A new regularization method is used to solve the overdetermined problem.

KW - finite element method

KW - Lagrange multiplier

KW - overdetermined two-velocity steady hydrodynamic system

UR - http://www.scopus.com/inward/record.url?scp=85042700920&partnerID=8YFLogxK

U2 - 10.1134/S1995423917040061

DO - 10.1134/S1995423917040061

M3 - Article

AN - SCOPUS:85042700920

VL - 10

SP - 347

EP - 357

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 4

ER -