Аңдатпа
Approaching of the solution of a static compressible medium to the solution of an incompressible mediumA well-known analogy of the flow of viscous incompressible fluid and incompressible elastic medium.According to this analogy, the solution of the equations of the elasticity theory with the Poisson's ratio ν = 0, 5 and for any fixed shear modulus µ can be interpreted as a motion of a viscous incompressible fluid with viscosity µ.Thus, we can consider the usual static linear elasticity task with Hooke's law at λ → ∞, as a mathematical model of approaching to incompressible medium.In this paper, we obtained the asymptotic λ → ∞.Estimation of the proximity of the solution of an elastic static problem with Hooke's law to the solution of incompressible medium (Stokes problem).The final estimate allows to use well-known difference schemes and algorithms for an elastic compressible medium to solve incompressible medium.In this paper, an estimate of the proximity of the solutions of these problems is proved at λ → ∞, i.e.λ→∞ .To substantiate this fact in [1-3], various methods for the first boundary value problem were investigated.For the static problem of the theory of elasticity, there is currently a whole series of papers devoted to numerical implementation using difference schemes.In paper [4], the estimate O(λ -α ) where k = 1 2 was obtained, in the proposed paper the estimate O(λ -1 ), and in further work we will show that this estimate is best possible in order.