Multigrid methods for the biharmonic equation using some nonconforming plate elements
نویسندگان
چکیده
منابع مشابه
Multigrid and Multilevel Methods for Nonconforming Elements
In this paper we systematically study multigrid algorithms and multilevel preconditioners for discretizations of second order elliptic problems using nonconforming rotated Q nite elements We rst derive optimal re sults for theW cycle and variable V cycle multigrid algorithms we prove that theW cycle algorithmwith a su ciently large number of smoothing steps con verges in the energy norm at a ra...
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We study the high-contrast biharmonic plate equation with HCT and Morley discretizations. We construct a preconditioner that is robust with respect to contrast size and mesh size simultaneously based on the preconditioner proposed by Aksoylu et al. (2008, Comput. Vis. Sci. 11, pp. 319–331). By extending the devised singular perturbation analysis from linear finite element discretization to the ...
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In this paper we study theoretical properties of multigrid algorithms and multilevel preconditioners for discretizations of second-order elliptic problems using nonconforming rotated Q1 finite elements in two space dimensions. In particular, for the case of square partitions and the Laplacian we derive properties of the associated intergrid transfer operators which allow us to prove convergence...
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In this paper we systematically study multigrid algorithms and multilevel preconditioners for discretizations of second order elliptic problems using nonconforming rotated Q nite elements We rst derive optimal re sults for the W cycle and variable V cycle multigrid algorithms we prove that theW cycle algorithm with a su ciently large number of smoothing steps con verges in the energy norm at a ...
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where u is the displacement and f 2 L( ) is the body force. Some of the simplest plate elements such as the Morley element (cf. [29]), the Zienkiewicz element (cf. [3]), the Fraeijs de Veubeke element (cf. [22]), the incomplete biquadratic element (cf. [34]) and the Adini element (cf. [1]) are nonconforming. Overlapping domain decomposition methods for nonconforming plate elements were studied ...
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ژورنال
عنوان ژورنال: The ANZIAM Journal
سال: 2001
ISSN: 1446-1811,1446-8735
DOI: 10.1017/s1446181100013079