Bicubic Hermite Elements in a Domain with the Curved Boundary

Abstract

A family of bicubic Hermite elements is considered which involves a rectangular element and two triangular ones including a triangular element with a curved side. The triangular elements are used in combination with the rectangular ones only near the boundary of a domain and provide interelement continuity of an approximate solution. Special attention is paid to the triangular element with a curved side since it is nonconforming in the sense of the Dirichlet boundary condition. For the Poisson equation the convergence estimate in the energy norm is proved.