Compatible approximation spaces for the velocity–pressure–stress formulation for creeping flows Original Research Article

The numerical approximation of the mixed velocity–pressure–stress formulation of the Stokes problem using spectral methods is considered. In addition to the compatibility condition between the discrete velocity and pressure spaces a second condition between the discrete velocity and stress spaces must also be satisfied in order to have a well-posed problem. The theory is developed by considering a doubly constrained minimization problem in which the viscous stress tensor is minimized subject to the constraint that the viscous forces are irrotational. Proper matching conditions between spectral elements are addressed leading to a discontinuous extra-stress approximation.