Preconditioning C1 Lagrange polynomial spline collocation method of elliptic equations by finite element method

摘要

This paper studies a preconditioning polynomial spline collocation method for an elliptic differential equation by a finite element stiffness matrix. For which, we first show that the decay rate of the C1 Lagrange polynomial spline increases with increasing degree and second show that the distribution of eigenvalues for the established preconditioning system is well bounded in terms of the number of unknowns for a fixed degree of polynomial spline.