TY - JOUR

T1 - Estimates of deviations from the exact solution of the Stokes problem in the vorticity-velocity-pressure formulation

AU - Mikhaylov, A.

AU - Repin, S.

PY - 2012/9/1

Y1 - 2012/9/1

N2 - The vorticity-velocity-pressure formulation for the stationary Stokes problem in 2D is considered. We analyze the corresponding generalized formulation, establish sufficient conditions that guarantee the existence of a generalized solution, and deduce estimates on the difference between the exact solution (i. e., the exact velocity, vorticity, and pressure) and an arbitrary approximating function (velocity, vorticity, pressure) that belongs to the corresponding functional class and satisfies the boundary conditions. For this purpose, we use the method suggested earlier by the second author, which is based on transformations of the integral identity that defines the corresponding generalized solution. Bibliography: 13 titles.

AB - The vorticity-velocity-pressure formulation for the stationary Stokes problem in 2D is considered. We analyze the corresponding generalized formulation, establish sufficient conditions that guarantee the existence of a generalized solution, and deduce estimates on the difference between the exact solution (i. e., the exact velocity, vorticity, and pressure) and an arbitrary approximating function (velocity, vorticity, pressure) that belongs to the corresponding functional class and satisfies the boundary conditions. For this purpose, we use the method suggested earlier by the second author, which is based on transformations of the integral identity that defines the corresponding generalized solution. Bibliography: 13 titles.

UR - http://www.scopus.com/inward/record.url?scp=84866892296&partnerID=8YFLogxK

U2 - 10.1007/s10958-012-0953-6

DO - 10.1007/s10958-012-0953-6

M3 - Article

AN - SCOPUS:84866892296

VL - 185

SP - 698

EP - 706

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 5

ER -