From compressible to incompressible materials via an asymptotic expansion

Summary. In linear elasticity problems, the pressure is usually introduced for computing the incompressible state. In this paper is presented a technique which is based on a power series expansion of the displacement with respect to the inverse of Lamé's coefficient . It does not require to introduce the pressure as an auxiliary unknown. Moreover, low degree finite elements can be used. The same technique can be applied to Stokes or Navier-Stokes equations, and can be extended to more general parameterized partial differential equations. Discretization error and convergence are analyzed and illustrated by some numerical results. Received April 21, 2000 / Revised version received February 28, 2001 / Published online October 17, 2001