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In this paper, we study the stability of the nonsymmetric version ofNitsche's method without penalty for compressible and incompressibleelasticity. For the compressible case we prove the convergence of the error inthe $H^1$- and $L^2$-norms. In the incompressible case we use a Galerkin leastsquares pressure stabilization and we prove the convergence in the $H^1$-normfor the velocity and convergence of the pressure in the $L^2$-norm.

A penalty free Nitsche type method for the weak imposition of boundary conditions in compressible and incompressible elasticity