BOUNDS ON SPECTRAL CONDITION NUMBERS OF MATRICES ARISING IN THE P-VERSION OF THE FINITE-ELEMENT METHOD

We estimate condition numbers of p-version matrices for tensor product elements with two choices of reference element degrees of freedom. In one case (Lagrange elements) the condition numbers grow exponentially in p, whereas in the other (hierarchical basis functions based on Tch ebycheff polynomials) the condition numbers grow rapidly but only alge braically in p. We conjecture that regardless of the choice of basis t he condition numbers grow like p4d or faster, where d is the dimension of the spatial domain.