Convergence rate estimates for iterative solutions of the biharmonic equation
The article is devoted to an analysis of the spectral radius of iteration matrices of finite-difference schemes approximating the biharmonic equation. The authors use the idea of \textit{P. R. Garabedian} [Math. Tables Aids Comput. 10, 183-185 (1956; Zbl 0073.108)] according to which the estimation of this radius in the form \(\rho =1-O(h^ k)\) can be reduced to the eigenvalue problem for some partial-differential operator. It is shown that the obtained estimates are precise for many classical iteration schemes. They can give also information on how much successful overrelaxation can improve the convergence rate. Some new iterative technics are suggested for which \(\rho =1-O(h)\).
scientific article; zbMATH DE number 4106204