EXPLICIT BOUNDS OF EIGENVALUES FOR STIFFNESS MATRICES BY QUADRATIC HIERARCHICAL BASIS METHOD)

The bounds for the eigenvalues of the stiffness matrices in the finite element discretization corresponding to Lu := - u" with zero boundary conditions by quadratic hierarchical basis are shown explicitly. The condition number of the resulting system behaves like O(1/h) where h is the mesh size. We also analyze a main diagonal preconditioner of the stiffness matrix which reduces the condition number of the preconditioned system to O(1).