Compatible approximation spaces for the velocity-pressure-stress formulation for creeping flows

The numerical approximation of the mixed velocity-pressure-stress formulati on of the Stokes problem using spectral methods is considered. In addition to the compatibility condition between the discrete velocity and pressure s paces a second condition between the discrete velocity and stress spaces mu st also be satisfied in order to have a well-posed problem. The theory is d eveloped by considering a doubly constrained minimization problem in which the viscous stress tensor is minimized subject to the constraint that the v iscous forces are irrotational. Proper matching conditions between spectral elements are addressed leading to a discontinuous extra-stress approximati on. (C) 2000 IMACS. Published by Elsevier Science B.V. All rights reserved.