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 \(\lambda\). 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.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received April 21, 2000 / Revised version received February 28, 2001 / Published online October 17, 2001
Rights and permissions
About this article
Cite this article
Guillaume, P., Masmoudi, M. & Zeglaoui, A. From compressible to incompressible materials via an asymptotic expansion. Numer. Math. 91, 649–673 (2002). https://doi.org/10.1007/s002110100347
Issue Date:
DOI: https://doi.org/10.1007/s002110100347