OPTIMAL MIXED H -- P FINITE ELEMENT METHODS FOR STOKES AND NON-NEWTONIAN FLOW

摘要

Based upon a new mixed variational formulation for the three-field Stokes equations and linearized Non-Newtonian flow, an h -- p finite element method is presented with or without a stabilization. As to the variational formulation without stabilization, optimal error bounds in h as well as in p are obtained. As with stabilization, optimal error bounds are obtained which is optimal in h and one order deterioration in p for the pressure, that is consistent with numerical results in [9, 12] and therefore solved the problem therein. Moreover, we proposed a stabilized formulation which is optimal in both h and p.