Parameter-free preconditioning for nearly-incompressible linear elasticity

James H. Adler, Xiaozhe Hu, Yuwen Li, Ludmil T. Zikatanov

Research output: Contribution to journalArticlepeer-review

Abstract

It is well known that via the augmented Lagrangian method, one can solve Stokes' system by solving the nearly incompressible linear elasticity equation. In this paper, we show that the converse holds, and approximate the inverse of the linear elasticity operator with a convex linear combination of parameter-free operators. In such a way, we construct a uniform preconditioner for linear elasticity for all values of the Lamé parameter λ∈[0,∞). Numerical results confirm that by using inf-sup stable finite-element spaces for the solution of Stokes' equations, the proposed preconditioner is robust in λ.

Original languageEnglish (US)
Pages (from-to)39-44
Number of pages6
JournalComputers and Mathematics with Applications
Volume154
DOIs
StatePublished - Jan 15 2024

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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