A conjugate gradient method and a multigrid algorithm for Morley's finite element approximation of the biharmonic equation
The numerical solution of the linear equations arising from Morley's nonconforming displacement method is studied. In the first part of the paper a preconditioning is established by which the condition number is reduced to \(O(h^{-1})\). Specifically, two Poisson equations are solved with each iteration step. The second part is concerned with a multigrid algorithm. Due to the nonconformity of the elements some non-standard ingredients are necessary. In particular, a transfer step and a stepsize control is incorporated. Convergence is proved under the assumption of \(H^ 3\)-regularity. Numerical results are included.
preconditioned conjugate gradient methods
Morley's nonconforming displacement method
scientific article; zbMATH DE number 3958645
scientific article