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Zbl 0877.73060
Arnold, Douglas N.; Falk, Richard S.; Winther, Ragnar
Preconditioning discrete approximations of the Reissner-Mindlin plate model. (English)
[J] RAIRO, Modélisation Math. Anal. Numér. 31, No.4, 517-557 (1997). ISSN 0764-583X

We consider iterative methods for the solution of the linear system of equations arising from the mixed finite element discretization of the Reissner-Mindlin plate model. We show how to construct a symmetric positive definite block diagonal preconditioner such that the resulting linear system has spectral condition number independent of both the mesh size $h$ and the plate thickness $t$. We further discuss how this preconditioner may be implemented and then apply it to solve the indefinite linear system. The presence of the small parameter $t$ and the fact that the matrix in the upper left corner of the partition is only positive semidefinite introduce new complications.

MSC 2000:: *74S05 Finite element methods
74K20 Plates
65F10 Iterative methods for linear systems

Keywords: symmetric positive definite block diagonal preconditioner; spectral condition number; plate thickness; indefinite linear system; small parameter

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