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

Abstract: In this paper, we study the stability of the nonsymmetric version of Nitsche's method without penalty for compressible and incompressible elasticity. For the compressible case we prove the convergence of the error in the $H<sup>1$- and $L<sup>2$-norms. In the incompressible case we use a Galerkin least squares pressure stabilization and we prove the convergence in the $H<sup>1$-norm for the velocity and convergence of the pressure in the $L<sup>2$-norm.