  The Nitsche method is a method of "weak imposition" of the inhomogeneous
Dirichlet boundary conditions for partial differential equations. This paper
explains stability and convergence study of the Nitsche method applied to
evolutionary diffusion-advection-reaction equations. We mainly discuss a
general space semidiscrete scheme including not only the standard finite
element method but also Isogeometric Analysis. Our method of analysis is a
variational one that is a popular method for studying elliptic problems. The
variational method enables us to obtain the best approximation property
directly. Actually, results show that the scheme satisfies the inf-sup
condition and Galerkin orthogonality. Consequently, the optimal order error
estimates in some appropriate norms are proven under some regularity
assumptions on the exact solution. We also consider a fully discretized scheme
using the backward Euler method. Numerical example demonstrate the validity of
those theoretical results.
