A Penalty-Free Nonsymmetric Nitsche-Type Method for the Weak Imposition of Boundary Conditions

In this paper we show that the nonsymmetric version of Nitsche's method for the weak imposition of boundary conditions is stable without penalty term. For nonconforming elements we prove the same result for the symmetric formulation as well. We prove optimal H¹-error estimates and L²-error estimates that are suboptimal with half an order in h. Both the pure diffusion and the convection--diffusion problems are discussed.