Each block can be replaced by a preconditioner in order to decrease the cost. Knowledge of the quality of this local preconditioner can be used directly in a study of the convergence rate of the overall iterative process. The Schur complement of an edge with respect to the variables interior to two adjacent elements is considered. The assembly and factorization of this block matrix are potentially expensive, especially for polynomials of high degree. It is demonstrated that the diagonal preconditioner of one such block has a condition number that increases approximately linearly with the degree of the polynomials.
Numerical results demonstrate that the actual condition numbers are relatively small.
65N35, 65N55 PII .