Mixing traction/pseudo-traction boundary conditions in incompressible flow
I was wondering if there is a way to incorporate the traction boundary conditions in discretizations using the pseudo-traction form of the Stokes problem or vice versa. Is there some literature on this or does one simply have no chance? I am mainly interested in finite-elements, but pointers to work dealing with other discretizations or publications dealing with both types of boundary conditions within one simulation would also be helpful.
Stress form of Stokes with pseudo-traction b.c.:
Pseudo-stress form of Stokes with traction b.c.:
I am aware that these boundary conditions are not natural in the respective (weak) formulations, but out of curiosity I would like to know if there are approaches to incorporate these boundary conditions anyway in a stable and convergent manner.
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