A STABILIZED TREATMENT OF THE BIHARMONIC OPERATOR WITH SPECTRAL METHODS

For the discretization of the biharmonic operator with spectral methods a high condition number like O(N8), where N is the maximal degree of polynomials, occurs. Two different techniques are proposed for reducing this condition number to O(N4). The best technique seems to be a splitting of the equation with the biharmonic operator into a system of two equations with the Laplace operator. An effective way of preconditioning is introduced. An effective iterative solver is presented.