A cascadic multigrid algorithm in the finite element method for the plane elasticity problem
- Gilyova, Lida V.
- Shaidurov, Vladimir V.
2010 Mathematics Subject Classification
- Elasticity problem, multigrid, cascadic algorithm, finite element method, conjugate-gradient method, Jacobi-type method
For the plane elasticity problem a standard scheme of the finite element method with the use of piecewise linear elements on triangles is discussed. For its solution on a sequence of embedded triangulations, a cascadic arrangement of two iterative algorithms is used, which gives the simplest version of multigrid methods without preconditioning and restriction onto a coarser grid. The cascadic algorithm begins on the coarsest grid where the grid problem is solved by direct method. To obtain approximate solutions on finer grids, the iterative method is used; interpolation of the approximate solution from the preceding coarser grid is taken as the initial guess. It is proved that the convergence rate of this algorithm does not depend on the number of unknowns and grids.