Iterative substructuring methods for spectral element discretizations of elliptic systems. II: Mixed methods for linear elasticity and stokes flow

Luca F. Pavarino, Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

Iterative substructuring methods are introduced and analyzed for saddle point problems with a penalty term. Two examples of saddle point problems are considered: The mixed formulation of the linear elasticity system and the generalized Stokes system in three dimensions. These problems are discretized with spectral element methods. The resulting stiffness matrices are symmetric and indefinite. The interior unknowns of each element are first implicitly eliminated by using exact local solvers. The resulting saddle point Schur complement is solved with a Krylov space method with block preconditioners. The velocity block can be approximated by a domain decomposition method, e.g., of wire basket type, which is constructed from a local solver for each face of the elements, and a coarse solver related to the wire basket of the elements. The condition number of the preconditioned operator is independent of the number of spectral elements and is bounded from above by the product of the square of the logarithm of the spectral degree and the inverse of the discrete inf-sup constant of the problem.

Original languageEnglish (US)
Pages (from-to)375-402
Number of pages28
JournalSIAM Journal on Numerical Analysis
Volume37
Issue number2
DOIs
StatePublished - 2000

Keywords

  • Gauss-Lobatto-Legendre quadrature
  • Linear elasticity
  • Mixed methods
  • Preconditioned iterative methods
  • Spectral element methods
  • Stokes problem
  • Substructuring

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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