Modeling of a Static Incompressible Medium

Abstract

In the article mathematical modeling of the solution of the static Stokes problem is considered by solving the static problem of the theory of elasticity, with Hooke’s law. We obtain estimates for the proximity of solutions of these problems under asymptotics, namely, when λ →∞, in this case the Poisson coefficient tends to 0,5, which corresponds to an incompressible medium. Further, it was proved that the estimate of the proximity of the solutions of the problems considered as unimprovable in order of 1/λ. This allows us to use previously differential schemes for the static problem of the theory of elasticity, as an approximate, it is obtained a method for solving the static Stokes problem on a sequence of grids.