Geodesic
Two multigrid iterative algorithms for a discrete analogue of the biharmonic equation
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 213-228 
L. V. Gilyova; V. V. Shaidurov. Two multigrid iterative algorithms for a discrete analogue of the biharmonic equation. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 3, pp. 213-228. http://geodesic.mathdoc.fr/item/SJVM_2004_7_3_a3/
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     title = {Two multigrid iterative algorithms for a~discrete analogue of the biharmonic equation},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A standard scheme of the finite element method with the use of bicubic elements on a rectangular quasiuniform grid is considered as applied to the two-dimensional Dirichlet problem for the biharmonic equation in a rectangle. To solve this scheme, two multigrid algorithms are treated on a sequence of embedded rectangular grids: a full multigrid with $V$-cycle and a simpler cascadic algorithm. The presence of angular points of a rectangle results in deficiency of solution smoothness which complicates substantiation of convergence of the algorithm as compared to a smooth case. At the same time, a number of arithmetical operations remains almost optimal for the cascadic algorithm and optimal for $V$-cycles.

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