Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries

We describe a practical procedure for the triangulation of arbitrary n-dimensional regular bounded domains by isoparametric simplicial elements preserving the optimal order of accuracy. Along similar lines we prove general error estimates for the finite element solution of second order elliptic problems. Various kinds of nonhomogeneous boundary conditions can be dealt with, such as Dirichlet, Neumann and Robin boundary conditions.