A non-standard FETI-DP mortar method for Stokes problem

Abstract

The trace spaces H 1/2 and H 1/2 00 play a key role in the FETI and mortar families of domain decomposition methods. However, a direct numerical evaluation of these norms is usually avoided. On the other hand, and for stability issues, the subspace of functions for which their jumps across the interfaces of neighbouring subdomains belong to these trace spaces yields a more suitable framework than the standard broken Sobolev space. Finally, the nullity of these jumps is usually imposed via Lagrange multipliers and using the pairing of the trace spaces with their duals. A direct computation of these pairings can be performed using the Riesz-canonical isometry. In this work we consider all these ingredients and introduce a domain decomposition method that falls into the FETI-DP mortar family. The application is to the incompressible Stokes problem and we see that continuous bounds are replicated at the discrete level. As a consequence, no stabilization is required. Some numerical tests are finally presented.