Shape calculus and finite element method in smooth domains

The use of finite elements in smooth domains leads naturally to polyhedral or piecewise polynomial approximations of the boundary. Hence the approxima tion error consists of two parts: the geometric part and the finite element part. We propose to exploit this decomposition in the error analysis by in troducing an auxiliary problem defined in a polygonal domain approximating the original smooth domain. The finite element part of the error can be tre ated in the standard way. To estimate the geometric part of the error, we n eed quantitative estimates related to perturbation of the geometry. WE deri ve such estimates using the techniques developed for shape sensitivity anal ysis.