대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제15권1호
  • /
  • Pages.143-153
  • /
  • 2000
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
권호 표지

BLOCK DIAGONAL PRECONDITIONERS FOR THE GALERKIN LEAST SQUARES METHOD IN LINEAR ELASTICITY

  • 발행 : 2000.01.01
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In [8], Franca and Stenberg developed several Galerkin least squares methods for the solution of the problem of linear elasticity. That work concerned itself only with the error estimates of the method. It did not address the related problem of finding effective methods for the solution of the associated linear systems. In this work, we propose the block diagonal preconditioners. The preconditioned conjugate residual method is robust in that the convergence is uniform as the parameter, v, goes to $\sfrac{1}{2}$. Computational experiments are included.

키워드

참고문헌

  1. Sobolev spaces R. A. Adams
  2. Studies in linear and nonlinear program-ming K. J. Arrow;L. Hurwicz;H. Uzawa
  3. SIAM J. Number. Anal. v.27 A taxonomy for conjugate gradient methods S. F. Ashby;T. A. Manteuffel;P. E. Saylor
  4. Number. Math v.56 A class of iterative methods for solving saddle point problems R. E. Bank;B. D. Welfert;H. Yserentant
  5. Mixed and hybrid finite element methods F. Brezzi;M. Fortin
  6. The finite element method for elliptic problems P. Ciarlet
  7. SIAM J. Numer. Anal. v.31 Inexact preconditioned Uzawa algorithms for saddle point problems H. Elman;G. Golub
  8. SIAM J. Numer. Anal. v.28 Error analysis of Galerkin least squares meth-ods for the elasticity equations L. P. Franca;R. Stenberg
  9. Iterative solution of large sparse systems of equations W. Hackbusch
  10. SIAM J. Sci. Comput. v.19 An optimal preconditioner for a class of saddle point prblems with a penalty term A. Klawonn
  11. SIAM J. Matrix Anal. Appl. v.13 A preconditioned iterative method for saddle point problems T. Rusten;R. Winther
  12. SIAM J. Numer. Anal. v.31 Fast iterative solutions of stabilized Stokes systems Part Ⅱ:Using general block preconditioners D. Sylvester;A. Wathen
  13. SIAM J. Numer. Anal. v.30 Fast iterative solution of stabilized Stokes systems Part Ⅰ:Using simple diagonal preconditioners A. Wathen;D. Sylvester